
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
Parallelogram $ABCD$ with $A(1,4)$, $B(3,8)$, $C(7,4)$, and $D(5,0)$ is reflected across the $y$-axis to $A'B'C'D'$ and then $A'B'C'D'$ is reflected across the line $y=x-1$ to $A''B''C''D''$. Determine the coordinates of the point $D''$.

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