
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 system of equations $\left\{\begin{array}{l} a=(b+c+d)^{3}, \\ b=(a+c+d)^{3}, \\ c=(a+b+d)^{3}, \\ d=(a+b+c)^{3} \end{array}\right.$ has how many real solutions.

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