
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 $ABC$ has vertices $A(3, 4)$, $B(5, 8)$, and $C(7, 4)$. It is first reflected across the $x$-axis to form triangle $A'B'C'$. Then, $A'B'C'$ is reflected across the line $y = -x + 1$. Find the coordinates of $C''$, the image of $C'$ after these transformations.

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