
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
Let the function $f(x) = 4^x + a \cdot 2^x + b$,
(1) If $f(0)=1$ and $f(-1)=-\frac{5}{4}$, find the explicit formula for $f(x)$;
(2) From (1), find the range of the function $f(x)$ when $0 \leq x \leq 2$.

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