
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 
\[ax+by=2,\]
\[ax^2+by^2=5,\]
\[ax^3+by^3=15,\]
and 
\[ax^4+by^4=35,\]
find \(ax^5+by^5.\)

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