
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 \( x_{i} \in \mathbf{R}^{+} \) \((i=1,2, \cdots, n)\), \( \sum_{i=1}^{n} x_{i} = m \), \( p, q \in \mathbf{R}^{+} \), and \( 2 \leqslant k \in \mathbf{N}^{+} \), find the maximum value of the function \( f(x) = \sum_{i=1}^{n} \sqrt[n]{p x_{i} + q} \).

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