
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 \( k_{1} \) be the smallest natural number that is a root of the equation

\[
\sin k^\circ = \sin 334 k^\circ
\]

(a) Find \( k_{1} \).

(b) Find the smallest natural number root of the same equation that is greater than \( k_{1} \).

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