
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 \( g \) is called extensive if \( g(x) + g(y) \geq x^2 + y^2 \) for all positive integers \( x \) and \( y \). Let \( h \) be an extensive function such that \( h(1) + h(2) + \dots + h(30) \) is as small as possible. Compute the minimum possible value for \( h(21) \).

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