
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 said to be sapid if $h(x) + h(y) > 2y^2$ for all positive integers $x$ and $y$. Let $j$ be a sapid function such that $j(1) + j(2) + \dots + j(30)$ is as small as possible. Compute the minimum possible value for $j(17)$.

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