
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 the numbers \( x_{1}, \ldots, x_{n} \in \left(0, \frac{\pi}{2}\right) \), find the maximum value of the expression

\[ 
A = \frac{\sin x_{1} + \ldots + \sin x_{n}}{\sqrt{\operatorname{tg}^{2} x_{1} + \ldots + \operatorname{tg}^{2} x_{n} + n}} 
\]

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