
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 the real numbers \(a, b, x, y\) satisfy the system of equations:
\[
\begin{cases}
a x + b y = 3, \\
a x^{2} + b y^{2} = 7, \\
a x^{3} + b y^{3} = 16, \\
a x^{4} + b y^{4} = 42,
\end{cases}
\]
find the value of \(a x^{5} + b y^{5}\).

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