
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
There exists a constant $c$ so that among all lines $\overline{PQ}$ of the parabola $y = 2x^2$ passing through $P = (0,c),$ the expression
\[ u = \frac{1}{PA^2} + \frac{1}{PB^2} \]is a fixed constant. Find the constant $u.$

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