
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
Let $x$, $y$, and $z$ be angles such that:
\begin{align*}
\sin x &= \cos y, \\
\sin y &= \cos z, \\
\sin z &= \cos x.
\end{align*}
Find the largest possible value of $\sin x$.

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