
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
Given a triangle $\triangle \mathrm{ABC}$ with internal angles $\angle A, \angle B, \angle C$ such that the smallest among $2 \angle A - \angle B$, $3 \angle B - 2 \angle C$, and $90^{\circ} - \angle A$ is $\alpha$, what is the maximum value of $\alpha$?

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