
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 \( a, b, x, \) and \( y \) that satisfy the following system of equations:

\[
\begin{cases}
a x + b y = 3, \\
a x^2 + b y^2 = 7, \\
a x^3 + b y^3 = 6, \\
a x^4 + b y^4 = 42,
\end{cases}
\]

find the value of \( a x^5 + b y^5 \).

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