
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 a, b, and c be Alice's, Bob's, and Charlie's ages, respectively. Given that four times Alice's age plus Bob's age equals three times Charlie's age, and that triple the cube of Charlie's age is equal to four times the cube of Alice's age added to the cube of Bob's age, and that their respective ages are pairwise coprime, compute the sum of the squares of their ages.

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