
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
Suppose point $P$ is on the curve represented by the equation $\sqrt{(x-5)^2+y^2} - \sqrt{(x+5)^2+y^2} = 6$, and $P$ is also on the line $y=4$. Determine the x-coordinate of point $P$.

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