
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 a point $P$, lines $e$ and $f$, and acute angles $\varepsilon$ and $\varphi$, construct the circles that pass through $P$ and intersect $e$ at an angle of $\varepsilon$ and $f$ at an angle of $\varphi$. (The angle between a circle and a line at their intersection point is the angle between the tangent to the circle at the intersection point and the line.)

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