
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 $LP = 15$ units and $SN = 75$ units, what is the area of square $PQRS$?
[asy]
draw((9,15.6)--(10.7,14.6)--(11.7,16.3));
draw((0,0)--(10,17.3)--(40,0)--cycle);
draw((5,0)--(20,0)--(20,15)--(5,15)--cycle);
label("$L$",(0,0),SW);
label("$P$",(5,0),S);
label("$R$",(20,0),S);
label("$N$",(40,0),SE);
label("$S$",(5,15),NW);
label("$Q$",(20,15),NE);
label("$M$",(10,17.3),N);
[/asy]

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