
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 circle C<sub>1</sub>: x<sup>2</sup> + y<sup>2</sup> - 2x - 4y - 4 = 0 and circle C<sub>2</sub>: x<sup>2</sup> + y<sup>2</sup> - 6x - 10y - 2 = 0, determine the number of common tangents of C<sub>1</sub> and C<sub>2</sub>.

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