
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
Let $f(x)$ be a function defined on $(−∞,+∞)$, such that for all $x∈R$, $f(x)+f(x+3)=0$, and when $-1 < x≤slant 1$, $f(x)=2x-3$.
(1) Find the period of $f(x)$;
(2) Find the analytic expression of $f(x)$ when $2 < x≤slant 4$.

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