
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
Find the minimum value of
$$
\max (a+b+c, b+c+d, c+d+e, d+e+f, e+f+g)
$$
subject to the constraints
(i) \( a, b, c, d, e, f, g \geq 0 \),
(ii) \( a+b+c+d+e+f+g=1 \).

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