
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 a function $f(x) = 4^x - a \cdot 2^x + b$. At $x=1$, $f(x)$ has a minimum value of $-1$;  
(1) Find the values of $a$ and $b$;  
(2) Find the set $A$ of $x$ values such that $f(x) \leq 35$.

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