
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
Consider all acute-angled triangles with a given side \(a\) and angle \(\alpha\).

What is the maximum of the sum of the squares of the lengths of the sides \(b\) and \(c\)?

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