
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
The non-negative numbers \(a, b, c, d, e, f, g\) have a sum of 1. Select the largest value among the sums \(a+b+c, b+c+d, c+d+e, d+e+f, e+f+g\). What is the minimum value of this largest sum obtained?

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