
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
A circle inscribed in an angle with vertex \( O \) touches its sides at points \( A \) and \( B \). The ray \( OX \) intersects this circle at points \( C \) and \( D \), with \( OC = CD = 1 \). If \( M \) is the intersection point of the ray \( OX \) and the segment \( AB \), what is the length of the segment \( OM \)?

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