
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 \( x_1, x_2, x_3, x_4, x_5 \) be non-negative real numbers such that \( x_1 + x_2 + x_3 + x_4 + x_5 = 100 \). Define \( M \) as the maximum of \( x_1 + x_2 \), \( x_2 + x_3 \), \( x_3 + x_4 \), and \( x_1 + x_3 \). What is the minimum value \( m \) that \( M \) satisfies?

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