
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 graph of the equation \[ 3x^2 + 7y^2 - 12x + 14y = k\] is a non-degenerate ellipse if and only if $k > a$. What is $a$?

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