
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the function \( y = f(x) \) for \( x \in \mathbb{R} \), with the conditions \( f(2) = 3 \) and that the derivative \( f'(x) \) satisfies \( f'(x) - 1 < 0 \) for all \( x \in \mathbb{R} \), find the solution set of the inequality \( f(x^2) < x^2 + 1 \).

Present the answer in LaTex format: \boxed{Your answer}
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