
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
Given real numbers \( a \), \( b \), \( x \), \( y \) that satisfy the equations \( a x + b y = 3 \), \( a x^{2} + b y^{2} = 7 \), \( a x^{3} + b y^{3} = 16 \), and \( a x^{4} + b y^{4} = 42 \), find the value of \( a x^{5} + b y^{5} \).

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