
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 $f(x)$ that satisfies $f(x+y)=f(x)+f(y)$ for any real numbers $x$ and $y$, and when $x > 0$, $f(x) < 0$, and $f(1) = -2$.

(1) Determine the parity of the function $f(x)$;

(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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