
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 $f(x)=-x^{2}+(a+4)x+2+b$, with $\log_{2}f(1)=3$, and $g(x)=f(x)-2x$ being an even function.
1. Find the analytical expression of the function $f(x)$.
2. If the maximum value of the function $f(x)$ in the interval $[m,+\infty)$ is $1-3m$, find the value of $m$.

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