
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 \( \mathrm{ABC} \), side \( AB = 4 \) and side \( BC = 6 \). Point \( M \) lies on the perpendicular bisector of segment \( AB \), and lines \( AM \) and \( AC \) are perpendicular. Find \( MA \), given that the circumradius of triangle \( ABC \) is 9.

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