
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 $ax+by=5,$ $ax^2+by^2=11,$ $ax^3+by^3=24,$ and $ax^4+by^4=58,$ find $ax^5+by^5.$

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