
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
The equations of the asymptotes of a hyperbola are \(y = 3x + 3\) and \(y = -3x - 1.\) Given that the hyperbola passes through the point \((2, 11),\) the standard form for the equation of the hyperbola is \[\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1,\] where \(a,\) \(b,\) \(h,\) and \(k\) are constants with \(a, b > 0.\) Find \(a + h.\)

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