
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
Let a function \( h \) be described as tenuous if for all pairs \( (x, y) \) of positive integers, \( h(x) + h(y) > (x+y)^2 \). Suppose \( h(1) + h(2) + \dots + h(30) \) is minimized. Find the minimum possible value of \( h(25) \).

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