
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]


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Given a point \( P(3,1) \) and two lines \( l_1: x + 2y + 3 = 0 \) and \( l_2: x + 2y - 7 = 0 \), find the equation of the circle passing through point \( P \) and tangent to lines \( l_1 \) and \( l_2 \).

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