
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 \(a,\) \(b,\) and \(c\) be angles such that
\begin{align*}
\cos a &= \tan b, \\
\cos b &= \tan c, \\
\cos c &= \tan a.
\end{align*}
Find the largest possible value of \(\sin a.\)

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