
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
A line passing through the center $M$ of the circle $M: (x+1)^{2}+y^{2}= \frac {7}{9}$ intersects the parabola $C: y^{2}=4x$ at points $A$ and $B$, and $\overrightarrow{MB}=3 \overrightarrow{MA}$. Find the minimum distance from point $A$ to any point on circle $M$.

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