
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
For an ellipse whose center is shifted to the point (3, -2) and with axes sizes changed, calculate the distance between the foci. The new semi-major axis is $a = 7$ and the new semi-minor axis is $b = 3$.

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