
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 $f(x)$ defined on $\mathbb{R}$ that satisfies: $f(a + b) = f(a) + f(b) - 1$ for any real numbers $a$ and $b$, and $f(x) > 1$ when $x > 0$. If $f(4) = 5$, find the solution set for the inequality $f(3x^2 - x - 2) < 3$.

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