
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 point $(x, y)$ is transformed into point $(3x, 3y)$ under the corresponding matrix transformation $M$.

1. Write out matrix $M$ and find its inverse matrix $M^{-1}$.
2. If curve $C$ is transformed into curve $C'$: $y^2 = 4x$ under the corresponding matrix transformation $M$, find the equation of curve $C$.

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