
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 that the minimum value of the quadratic function $f(x)$ is 1, and it satisfies $f(0) = f(4) = 9$.
1. Find the analytical expression of $f(x)$;
2. If $f(x)$ has a minimum value of $g(m)$ on the interval $[m, m+2]$, find the expression of the function $g(m)$.

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