
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 $f(x)$ defined on $\mathbb{R}$ that satisfies $f(x+y)=f(x)+f(y)$ for any $x$, $y$, and $f(1)=-2$, and $f(x) < 0$ when $x > 0$.
(1) Determine the parity of $f(x)$ and provide a proof;
(2) Solve the inequality $f(x+\#)+f(2x-x^{2}) > 2$ with respect to $x$.

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