
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 the interval $[-1,1]$, given that the expression for $x \in [-1,0]$ is $f(x)= \dfrac {1}{4^{x}}- \dfrac {a}{2^{x}}(a\in\mathbb{R})$.  
$(1)$ Write the expression for $f(x)$ 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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