
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
Triangle \(DEF\) has vertices \(D(3, 3)\), \(E(6, -1)\), and \(F(3, -1)\). This triangle is reflected over the x-axis and then rotated \(90^\circ\) counterclockwise around the origin. What are the coordinates of point \(F'\) after these transformations?

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