
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
(For this question, the full score is 13 points) Define the odd function $f(x)$ on the interval $[-1,1]$, it is known that the expression of $f(x)$ when $x \in [-1,0]$ is $f(x) = -a$ ($a \in \mathbb{R}$).  
(1) Write the expression of $f(x)$ on the interval $[0,1]$.  
(2) Find the maximum value of $f(x)$ on the interval $[0,1]$.

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