
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
A function $f(x)$ is defined on $R$ and satisfies $f(x) + f(-x) = 0$. When $x < 0$, $f(x) = \left(\frac{1}{4}\right)^x - 8 \times \left(\frac{1}{2}\right)^x - 1$.
(1) Find the analytical expression of $f(x)$;
(2) Find the maximum and minimum values of $f(x)$ when $x \in [1, 3]$.

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