
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
Points $A(3, -2), B(5, -5)$, and $C(2, -4)$ are the vertices of $\triangle ABC$. Translate $\triangle ABC$ by moving it 4 units to the right and 3 units up, and then rotate it 180 degrees around the point $(4, 0)$. What will be the coordinates of the image of point A after these transformations?

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