
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
Let $T_1$ be a transformation that represents a counterclockwise rotation of $\frac{\pi}{2}$, with its corresponding transformation matrix given by $M_1$; and let $T_2$ be another transformation with its corresponding transformation matrix given by $M_2 = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$.
(I) Find the coordinates of the point $P'(x', y')$ after applying $T_1$ to the point $P(2,1)$.
(II) Find the equation of the curve obtained by successively applying transformations $T_1$ and $T_2$ to the graph of the function $y = x^2$.

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