
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 base of a right prism $ABC A_{1}B_{1}C_{1}$ is a triangle with $|AB|=|AC|$ and $\widehat{ABC}=\alpha$. Additionally, point $D$ is the midpoint of edge $AA_{1}$, $\widehat{DCA}=\beta$, and $|CD|=b$. Find the lateral surface area of the prism.

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