
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
If $a$, $b$, $x$, and $y$ are real numbers such that $2ax + 2by = 6$, $3ax^2 + 3by^2 = 21$, $4ax^3 + 4by^3 = 64$, and $5ax^4 + 5by^4 = 210$, find $6ax^5 + 6by^5$.

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