
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
Let $F$ be the focus of the parabola $y^2=4x$, and let $A$ be a point on the parabola. Let $B$ be any point on the circle $C: (x+3)^2+(y+3)^2=4$. If the distance from point $A$ to the $y$-axis is $m$, then the minimum value of $m+|AB|$ is $\boxed{2}$.

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