
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 that \(a, b, x, y\) satisfy the following system of equations:
\[
\left\{
\begin{array}{l}
a x + b y = 3, \\
a x^2 + b y^2 = 7, \\
a x^3 + b y^3 = 16, \\
a x^4 + b y^4 = 42,
\end{array}
\right.
\]
find the value of \(a x^5 + b y^5\).

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