
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
Twice Jake's age plus three times Amy's age equals four times Ryan's age. 
If the sum of the cube of Jake's age and the cube of Amy's age equals half the cube of Ryan's age, plus they collectively hold a total age of 50 years, then find the sum of the cubes of their ages.
A) 24680
B) 22100
C) 29000
D) 15000
E) 32000

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