
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 $n > 8$ be an integer, and suppose $n$ is a root of the equation $x^2 - cx + d = 0$. If the coefficient $c$ in a base-$n$ number system is represented as $21$, what is the base-$n$ representation of $d$?
**A)** $110$  
**B)** $101$  
**C)** $111$  
**D)** $120$  
**E)** $210$

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