
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 point \( M \) inside a circle divides the chord of this circle into segments equal to \( a \) and \( b \). A chord \( AB \) passes through point \( M \) and is bisected by \( M \). Find \( AB \).

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