
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
Circles  $k_1$  and  $k_2$  with radii  $r_1=6$  and  $r_2=3$  are externally tangent and touch a circle  $k$  with radius  $r=9$  from inside. A common external tangent of  $k_1$  and  $k_2$  intersects  $k$  at  $P$  and  $Q$ . Determine the length of  $PQ$ .

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