
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 numbers $x_{1}, \ldots, x_{n}, y_{1}, \ldots, y_{n}$ satisfy the condition $x_{1}^{2}+\ldots+x_{n}^{2}+y_{1}^{2}+\ldots+y_{n}^{2} \leqslant 1$. Find the maximum value of the expression

$$
A=\left(3\left(x_{1}+\ldots+x_{n}\right)-5\left(y_{1}+\ldots+y_{n}\right)\right) \cdot\left(5\left(x_{1}+\ldots{x_{n}}\right)+3\left(y_{1}+\ldots{y_{n}}\right)\right)
$$

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