
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 \( c \) and \( d \) be real numbers such that
\[ c^3 - 18c^2 + 27c - 100 = 0 \quad \text{and} \quad 9d^3 - 81d^2 - 324d + 3969 = 0. \]
Compute \( c + d. \)

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