
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 $f\left(\log _{2}x\right)=ax^{2}-2x+1-a$, where $a\in \mathbb{R}$.
1. Find the analytical expression of $f\left(x\right)$.
2. Solve the equation $f\left(x\right)=(a-1)\cdot 4^{x}$.

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