
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 \( y^{2}=4(x-1) \) with its vertex at point \( M \):
(1) The center of circle \( C \) is symmetrical to the vertex \( M \) with respect to the \( y \)-axis, and circle \( C \) is tangent to the \( y \)-axis. Find the equation of circle \( C \);
(2) From any point \( N \) on the parabola, two tangents are drawn to circle \( C \). These tangents intersect the directrix of the parabola at points \( A \) and \( B \). Find the range of values for \( |AB| \).

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