To solve this fill-in-the-blanks question, we need to choose the grammatically correct and contextually appropriate words from the given options. Let's break down the sentence:

Peace and stability cannot be achieved unless progress is made toward _____ solutions to the world's most _____ problems, including poverty.

The first blank requires a word that fits after the preposition "toward". In English, prepositions like "toward" are typically followed by a noun or a gerund (a verb form ending in "-ing" that functions as a noun). Therefore, "finding" (a gerund) is the correct choice here, not the infinitive "to find".

The second blank requires an adjective to describe the noun "problems". The word "pressing" is an adjective meaning "requiring quick or immediate action; urgent". This fits the context of serious global issues like poverty. The word "pressed" is a verb form (past tense or past participle) and is not used as an adjective to describe problems in this way.

Step-by-Step Reasoning:

Step 1: Analyze the first blank. The preposition "toward" must be followed by a noun. "Finding" is a gerund (acting as a noun), while "to find" is an infinitive (acting as a verb). The correct grammatical structure is "toward finding solutions".

Step 2: Analyze the second blank. We need an adjective to modify "problems". "Pressing" is an adjective meaning urgent. "Pressed" is not an adjective; it is the past tense of the verb "to press" and does not fit this context.

Final Answer: The correct option is finding / pressing.

Related Grammar Concepts

Gerunds after Prepositions: A gerund is the -ing form of a verb that functions as a noun. Prepositions (e.g., toward, of, for, by) are almost always followed by a gerund, not an infinitive. For example: "He is good at swimming", "I am thinking about buying a car".

Adjectives vs. Verb Forms: It is important to distinguish between adjectives and other parts of speech. An adjective describes a noun (e.g., a pressing issue). A past participle can sometimes be used as an adjective (e.g., a broken window), but "pressed" is not conventionally used as an adjective to describe a problem; "pressing" is the standard term.

Key Formulae/Rules

Rule 1: Preposition + Gerund

Formula: $\text{Preposition}+\text{Verb}-\mathrm{ing}(\text{Gerund})$

Rule 2: Adjective-Noun Agreement

Formula: $\text{Article}+\text{Adjective}+\text{Noun}$