
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

The distance between the centers $O_{1}$ and $O_{2}$ of the circles $\omega_{1}$ and $\omega_{2}$ is $5r$, and their radii are $r$ and $7r$ respectively. A chord of the circle $\omega_{2}$ touches the circle $\omega_{1}$ and is divided by the point of tangency in the ratio $1:6$. Find the length of this chord.

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