
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 $ABCD$ has vertices $A(1,3)$, $B(3,8)$, $C(7, 6)$, and $D(5, 1)$. It is first reflected over the $y$-axis, producing parallelogram $A'B'C'D'$, and then $A'B'C'D'$ is reflected over the line $y = -x$ to form $A''B''C''D''$. What is the ordered pair of $D''$ in the coordinate plane?

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