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

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