
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 the graph of the parabola $y=_ax^2+_bx+_c$ is obtained by shifting the graph of $y=−_x^2+4$ one unit to the right, and then reflecting it about the $y$-axis.

(1) Find the equation of the parabola after these transformations.

(2) If the parabola obtained in (1) intersects the $x$-axis at point $B$ on the left side of the symmetry axis, and at point $A$ on the right side, and intersects the $y$-axis at point $C$. If $P$ is a moving point on the symmetry axis of the parabola, find the coordinates of point $P$ such that $△BPC$ is a right triangle.

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