
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
Consider a hyperbola where the center is at $(3, 1)$, one focus is at $(3, 10)$, and one vertex is at $(3, 4)$. The equation of this hyperbola can be expressed as
\[\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1.\]
Find the sum $h + k + a + b$.

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