
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 a rectangle $PQRS$, $PQ = 4$ cm, $QR = 10$ cm, and $PM = MQ$. The area of triangle $PMQ$ is half the area of rectangle $PQRS$. What is the length in centimeters of segment $MQ$?

[asy]
draw((0,0)--(0,40)--(16,40)--(16,0)--cycle);
draw((16,40)--(8,40)--(8,0));
label("$P$",(0,40),W);
label("$Q$",(0,0),W);
label("$R$",(16,0),E);
label("$S$",(16,40),E);
label("$M$",(8,40),N);
[/asy]

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