
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 two tangent circles $c_{1}$ and $c_{2}$, point $P$ lies on the radical axis, which is the common tangent line perpendicular to the line connecting their centers. Using a compass and a straightedge, try to construct all circles $c$ that are tangent to both $c_{1}$ and $c_{2}$ and pass through point $P$.

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