
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 positive real solutions to: \begin{eqnarray*} (x_1^2-x_3x_5)(x_2^2-x_3x_5) &\le& 0  (x_2^2-x_4x_1)(x_3^2-x_4x_1) &\le& 0  (x_3^2-x_5x_2)(x_4^2-x_5x_2) &\le& 0  (x_4^2-x_1x_3)(x_5^2-x_1x_3) &\le & 0  (x_5^2-x_2x_4)(x_1^2-x_2x_4) &\le& 0  \end{eqnarray*}

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