
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
For each real number $a$ where $0 \leq a \leq 1$, let $x$ and $y$ be chosen independently at random from the intervals $[0, a]$ and $[0, 1-a]$, respectively. Let $Q(a)$ be the probability that \(\sin^2{(\pi x)} + \sin^2{(\pi y)} > 1\). What is the maximum value of $Q(a)$?
A) 0.75  
B) 0.85  
C) 0.90  
D) 0.95

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