
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 an ellipse with the following equation:
\[\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1\]
where the center of the ellipse has been shifted to \((3, -5)\), the semi-major axis length is 7, and the semi-minor axis length is 4. Further, the distance of the foci from the center is calculated using \(c = \sqrt{a^2 - b^2}\). Determine the value of \(h + k + a + b + 2c\).

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