
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 that the graph of the odd function $f(x)$ on $R$ is symmetric about the line $x=1$, and $f\left(x\right)= \frac{1}{2}x$ when $x∈[0,1]$.

(1) Find the value of $f\left( \frac{15}{2}\right)$;

(2) Find the analytical expression of $f(x)$ when $x∈[-1,3]$;

(3) If $f\left(x\right)=- \frac{1}{2}$, find the value of $x$.

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