
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 equation of an ellipse is given, which is rotated by 45 degrees, and can be expressed as follows:
\[\frac{((x - h)\cos\theta + (y - k)\sin\theta)^2}{a^2} + \frac{(-(x - h)\sin\theta + (y - k)\cos\theta)^2}{b^2} = 1.\]
Given that the center of the ellipse is at \((-2, 3)\), the semi-major axis is 6, and the semi-minor axis is 4, and knowing the rotation angle \(\theta = 45^\circ\), find the sum \(h + k + a + b\).

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