
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 equation of a circle is \(x^{2}+y^{2}=4\), if a parabola passes through points \(A(-1,0)\), \(B(1,0)\) and uses the tangent line of the circle as the directrix, then the equation of the locus of the focus of the parabola is __________.

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