
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

Given the distribution function of a two-dimensional random variable:

$$
F(x, y)=\left\{\begin{array}{c}
\sin x \cdot \sin y \text { for } 0 \leq x \leq \pi / 2, 0 \leq y \leq \pi / 2 \\
0 \quad \text { for } x<0 \text { or } y<0
\end{array}\right.
$$

Find the probability that the random point $(X, Y)$ falls within the rectangle bounded by the lines $x=0, x=\pi / 4, y=\pi / 6, y=\pi / 3$.

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