
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 points $A$, $B$, and $C$ on a plane and an angle $\varphi$, construct a circle $k$ that passes through points $A$ and $B$ and appears at an angle $\varphi$ from point $C$; i.e., the angle between the tangents drawn from $C$ to the circle $k$ is $\varphi$.

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