
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 \(ax+by=5\), \(ax^2 + by^2 = 9\), \(ax^3 + by^3 = 22\), and \(ax^4 + by^4 = 60\). Find \(ax^5 + by^5\).

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