
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
A sequence $(c_n)$ is defined as follows: $c_1 = 2,$ $c_2 = 1,$ and
\[c_n = \frac{2 - c_{n - 1}}{3c_{n - 2}}\] for all $n \ge 3.$ Find $c_{100}$.

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