
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
In the same Cartesian coordinate system, a dilation transformation that turns the line $x-2y=2$ into the line $2x'-y'=4$ is given by 
$$
\begin{cases}
x' = \lambda x \\
y' = \mu y
\end{cases}
$$
Calculate the value of $\lambda + \mu$.

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