
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
A function  $g: \mathbb{Z} \to \mathbb{Z}$  is called adjective if  $g(m)+g(n)>max(m^2,n^2)$  for any pair of integers  $m$  and  $n$ . Let  $f$  be an adjective function such that the value of  $f(1)+f(2)+\dots+f(30)$  is minimized. Find the smallest possible value of  $f(25)$ .

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