
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 $f(x)$ is an odd function, and for any $x$ in its domain, it satisfies $f(1-x)=f(1+x)$. When $x \in (0,1]$, $f(x) = e^x$. Determine $f(x)$ when $x \in [-1,0)$ and when $x \in (4k, 4k+1]$, where $k \in \mathbb{N}^*$.

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