
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 \( x_i \in \mathbb{R}, x_i \geq 0 \) for \( i=1,2,3,4,5 \), and \( \sum_{i=1}^{5} x_i = 1 \), determine the minimum value of \( \max \{ x_1 + x_2, x_2 + x_3, x_3 + x_1, x_4 + x_5 \} \).

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