
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
An integer-valued function $h$ is called tenuous if $h(x) + h(y) > 2y^2$ for all positive integers $x$ and $y.$ Let $h$ be a tenuous function such that $h(1) + h(2) + \dots + h(30)$ is as small as possible. Compute the minimum possible value for $h(25).$

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