
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 a function $f(x)$ for any real numbers $x$, $y$ always satisfies $f(x+y) = f(x) + f(y)$, and when $x > 0$, $f(x) < 0$, and $f(1) = -2$,
1. Determine the parity of $f(x)$;
2. Find the maximum value of $f(x)$ in the interval [-3, 3];
3. Solve the inequality $f(ax^2) - 2f(x) < f(ax) + 4$ with respect to $x$.

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