
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  $ax + by = 3,$   $ax^2+by^2=7,$   $ax^3+bx^3=16$ , and  $ax^4+by^4=42,$  find  $ax^5+by^5$ .

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