
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 all quadruples of real numbers \((a, b, c, d)\) satisfying the system of equations

\[
\left\{\begin{array}{l}
(b+c+d)^{2010}=3 a \\
(a+c+d)^{2010}=3 b \\
(a+b+d)^{2010}=3 c \\
(a+b+c)^{2010}=3 d
\end{array}\right.
\]

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