
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 a rectangular parallelepiped $A B C D A_1 B_1 C_1 D_1$, the diagonals $A C$ and $B D$ of the base $A B C D$ intersect at point $M$, and $\angle A M B = \alpha$. Find the lateral surface area of the parallelepiped if $B_1 M = b$ and $\angle B M B_1 = \beta$.

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