
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 function $f(x)$ is an odd function defined on $\mathbb{R}$, its graph is symmetric about the line $x=1$, and $f(x) = x$ for $0 < x \leq 1$, determine the analytic expression for $y = f(x)$ when $x \in (5, 7]$.

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