
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 point M(3, $y_0$) is on the parabola $y^2=2px$ ($0<p<6$), and the distance from M to the focus of the parabola is twice the distance from M to the line $x= \frac{p}{2}$, find the value of $p$.

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