
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
Define an odd function $f(x)$ on $[-a,a] (a > 0)$. The analytical expression of $f(x)$ when $x \in [-a,0]$ is given by $f(x)= \frac{m}{{e}^{2x}}+ \frac{1}{{e}^{x}}$, where $e$ is the base of the natural logarithm.

(1) Write the analytical expression of $f(x)$ on $[0,a]$;

(2) Find the maximum value $M(a)$ of $f(x)$ on $[0,a]$.

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