
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
In the space rectangular coordinate system $Oxyz$, given points $A(2,0,0)$, $B(2,2,0)$, $C(0,2,0)$, and $D(1,1,\sqrt{2})$. Determine whether $S_1=S_2=S_3$, $S_2=S_1$ and $S_2 \ne S_3$, $S_3=S_1$ and $S_3 \ne S_2$, or $S_3=S_2$ and $S_3 \ne S_1$, where $S_1$, $S_2$, and $S_3$ are the areas of the orthogonal projection of the tetrahedron $D-ABC$ on the coordinate planes $xOy$, $yOz$, and $zOx$ respectively.

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