
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 $C_a$ and $C_b$ are externally tangent, and they are both internally tangent to circle $C_c$. The radii of $C_a$ and $C_b$ are 5 and 12, respectively, and the centers of the three circles are all collinear. A chord of $C_c$ is also a common external tangent of $C_a$ and $C_b$. Find the length of the chord in its simplest form.

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