
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 the function $f(x)=1-2a^{x}-a^{2x}$ where $a>1$:
1. Find the range of the function $f(x)$.
2. If the minimum value of the function $f(x)$ is $-7$ when $x\in [-2,1]$, determine the value of $a$ and the maximum value of the function $f(x)$.

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