
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
Let  $ABC$  be a right triangle where  $\measuredangle A = 90^\circ$  and  $M\in (AB)$  such that  $\frac{AM}{MB}=3\sqrt{3}-4$ . It is known that the symmetric point of  $M$ with respect to the line  $GI$  lies on  $AC$ . Find the measure of  $\measuredangle B$ .

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