
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 the real numbers \( a, b, c, d, e \) that satisfy the system of equations:
$$
\left\{\begin{array}{l}
a b + a c + a d + a e = -1, \\
b c + b d + b e + b a = -1, \\
c d + c e + c a + c b = -1, \\
d e + d a + d b + d c = -1, \\
e a + e b + e c + e d = -1,
\end{array}\right.
$$

find all possible values of \( a \).

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