
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 $a$, $b$, $x$, and $y$ be real numbers such that $2ax + 3by = 6$, $2ax^2 + 3by^2 = 14$, $2ax^3 + 3by^3 = 33$, and $2ax^4 + 3by^4 = 87$. Determine $2ax^5 + 3by^5$.

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