
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
Let \( x_1, x_2, \cdots, x_n \geqslant 0 \) and \( x_1 + x_2 + \cdots + x_n \geqslant k \), where \( k \) is a positive constant. Find the maximum value of \( f\left(x_1, x_2, \cdots, x_n\right) = \frac{x_1 \sqrt{\sum_{i=1}^{n} x_i}}{\left(\sum_{i=1}^{n-1} x_i\right)^2 + x_n} \).

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