
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 the real numbers \( a, b, c, d, e \) be such that \( a, b, c, d, e \geq -1 \) and \( a + b + c + d + e = 5 \). Find the minimum and maximum values of 
$$
S = (a+b)(b+c)(c+d)(d+e)(e+a)
$$

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