
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  $x$  be a positive real number. Define
\[
  A = \sum_{k=0}^{\infty} \frac{x^{3k}}{(3k)!}, \quad
  B = \sum_{k=0}^{\infty} \frac{x^{3k+1}}{(3k+1)!}, \quad\text{and}\quad
  C = \sum_{k=0}^{\infty} \frac{x^{3k+2}}{(3k+2)!}.
\] Given that  $A^3+B^3+C^3 + 8ABC = 2014$ , compute  $ABC$ .

*Proposed by Evan Chen*

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