
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 number of solutions in non-negative reals to the following equations: 
\begin{eqnarray*}x_1 + x_n ^2 = 4x_n  x_2 + x_1 ^2 = 4x_1  ...  x_n + x_{n-1}^2 = 4x_{n-1} \end{eqnarray*}

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