
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 determinant $\begin{vmatrix} 2^{x} & 7 & 4^{x}\\ 4 & -3 & 4\\ 6 & 5 & -1\\ \end{vmatrix}$, let $f(x)$ be the algebraic cofactor of the element in the third row and second column. Find the zero(s) of the function $y=1+f(x)$.

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