
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 \( ax + by = 4, \) \( ax^2 + by^2 = 9, \) \( ax^3 + by^3 = 23, \) and \( ax^4 + by^4 = 54, \) find \( ax^5 + by^5 \).

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