
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 \(x_{i} \in \mathbf{R}_{+}\) for \(i=1,2,3,4,5\), find the minimum value of:

\[f = \frac{x_{1}+x_{3}}{x_{5}+2 x_{2}+3 x_{4}} + \frac{x_{2}+x_{4}}{x_{1}+2 x_{3}+3 x_{5}} + \frac{x_{3}+x_{5}}{x_{2}+2 x_{4}+3 x_{1}} + \frac{x_{4}+x_{1}}{x_{3}+2 x_{5}+3 x_{2}} + \frac{x_{5}+x_{2}}{x_{4}+2 x_{1}+3 x_{3}}.\]

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