
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
Determine all positive real solutions of the following system of equations:

$$
\begin{aligned}
& a=\max \left\{\frac{1}{b}, \frac{1}{c}\right\} \\
& b=\max \left\{\frac{1}{c}, \frac{1}{d}\right\} \\
& c=\max \left\{\frac{1}{d}, \frac{1}{e}\right\} \\
& d=\max \left\{\frac{1}{e}, \frac{1}{f}\right\} \\
& e=\max \left\{\frac{1}{f}, \frac{1}{a}\right\} \\
& f=\max \left\{\frac{1}{a}, \frac{1}{b}\right\}
\end{aligned}
$$

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