
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
In triangle \(ABC\), it is known that \(\angle A=120^{\circ}\), side \(AC=1\) and side \(BC=\sqrt{7}\). On the extension of side \(CA\), point \(M\) is taken such that \(BM\) is the altitude of triangle \(ABC\). Find the radius of the circle passing through points \(A\) and \(M\) and touching the circle passing through points \(M\), \(B\), and \(C\) at point \(M\).

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