
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
From point \( M \), located outside a circle at a distance \( \sqrt{7} \) from the center, a secant is drawn, where the internal part is twice as short as the external part and is equal to the radius of the circle.

Find the radius of the circle.

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