
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
Points $P$, $Q$, $R$, and $S$ are midpoints of the sides of a larger square. If the area of the larger square is 100, what is the area of the smaller square formed by connecting these midpoints? [asy]
pair p=(0,1),q=(1,0),r=(0,-1),s=(-1,0);
draw((-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle);
draw(p--q--r--s--cycle);
label("$P$", p, N);
label("$Q$", q, E);
label("$R$", r, S);
label("$S$", s, W);
[/asy]

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