
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 is a moving point on the parabola $y^2=8x$, F is the focus of the parabola, and point A is on the circle $C: (x-3)^2+(y+1)^2=1$, then the minimum value of $|AM|+|MF|$ is.

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