
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
Suppose $a, b, x,$ and $y$ are real numbers and the equations $ax + by = 1$, $ax^2 + by^2 = 9$, $ax^3 + by^3 = 28$, and $ax^4 + by^4 = 96$ hold. Determine the value of $ax^5 + by^5$.

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