
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
Suppose \( x, y, z \) and \( \lambda \) are positive real numbers such that
\[ 
\begin{aligned}
yz & = 6\lambda x \\
xz & = 6\lambda y \\
xy & = 6\lambda z \\
x^2 + y^2 + z^2 & = 1
\end{aligned}
\]
Find the value of \( (xyz\lambda)^{-1} \).

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