
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
In the sequence $\left\{a_{n}\right\}$, if the adjacent terms $a_{n}$ and $a_{n+1}$ are the two roots of the quadratic equation
$$
x_{n}^{2} + 3n x_{n} + c_{n} = 0 \quad (n = 1, 2, \cdots)
$$
then when $a_{1} = 2$, what is the value of $c_{100}$?

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