
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
A semicircle has diameter  $XY$ . A square  $PQRS$  with side length 12 is inscribed in the semicircle with  $P$  and  $S$  on the diameter. Square  $STUV$  has  $T$  on  $RS$ ,  $U$  on the semicircle, and  $V$  on  $XY$ . What is the area of  $STUV$ ?

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