
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
Given that $A$ is a point on the parabola $C:y^{2}=2px\left(p \gt 0\right)$, the distance from point $A$ to the focus of $C$ is $12$, and the distance to the $y$-axis is $9$. Find the value of $p$.

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