
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 defined on $[-1, 1]$, and its analytical expression when $x \in [-1, 0]$ is $f(x) = \frac{1}{4^x} - \frac{b}{2^x}$ ($b \in \mathbb{R}$).
(I) Find the value of $b$ and the analytical expression of $f(x)$ on $[0, 1]$;
(II) Find the maximum and minimum values of $f(x)$ on $[0, 1]$.

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