
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 $C: y^{2}=4x$ with the directrix $l$, point $M$ is a point on the parabola, and the circle with center $M$ passes through the point $A(3,0)$ and is tangent to the line $l$, determine the length of the chord obtained when the circle intersects the $y$-axis.

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