
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 vertices $A(2,5)$, $B(4,9)$, $C(6,5)$, and $D(4,1)$ is reflected across the $x$-axis resulting in $A'B'C'D'$. Subsequently, $A'B'C'D'$ is reflected across the line $y=x-1$ resulting in $A''B''C''D''$. If $D'$ is the reflection of $D$ and $D''$ the reflection of $D'$ across the new line, what is the ordered pair of $D''$ in the coordinate plane?

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