
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 the quadratic function y = (x - m)² - 2(x - m) (where m is a constant),

1. Find the coordinates of the points where the graph of the function intersects the x-axis.
2. Find the coordinates of the vertex P of the graph of the function.
3. If the graph of the function is shifted 3 units to the left and then 1 unit upwards to obtain the graph of the function y = x², directly write out the value of m.

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