
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 the parabola $E$: $y^{2}=2px (p > 0)$ with focus $F$, let $M$ be a point on the parabola $E$. The minimum value of $|MF|$ is $2$. If $P$ is any point on the parabola $E$ and $A(4,1)$, determine the minimum value of $|PA|+|PF|$.

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