
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 $f(x)=x^{2}-5x+7$, for any positive integer $n$, there exist $m+1$ real numbers $a_0, a_1, a_2, \ldots, a_m$ in the interval $[1, n+\frac{5}{n}]$ such that $f(a_0) > f(a_1) + f(a_2) + \ldots + f(a_m)$ holds. Find the maximum value of $m$.

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