
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 ellipse is defined by the equation 
\[\frac{x^2}{36} + \frac{y^2}{16} = 1.\]
A chord $\overline{CD}$ passes through a focus \(G\) of the ellipse. If \(CG = 2\), find \(DG\).

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