
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
Square $PQRS$ is inscribed in right triangle $LMN$, as shown below. If $LP = 30$ units and $SN = 70$ units, what is the area of square $PQRS$?
[asy]
draw((9,15.6)--(10.7,14.6)--(11.7,16.3));
draw((0,0)--(11,20)--(50,0)--cycle);
draw((9,0)--(26,0)--(26,17)--(9,17)--cycle);
label("$L$",(0,0),SW);
label("$P$",(9,0),S);
label("$S$",(26,0),S);
label("$N$",(50,0),SE);
label("$Q$",(9,17),NW);
label("$R$",(26,17),NE);
label("$M$",(11,20),N);
[/asy]

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