
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
Two lines passing through point \( M \), which lies outside the circle with center \( O \), touch the circle at points \( A \) and \( B \). Segment \( OM \) is divided in half by the circle. In what ratio is segment \( OM \) divided by line \( AB \)?

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