
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 the rectangular coordinate system $xOy$, the coordinates of point $A\left(x_{1}, y_{1}\right)$ and point $B\left(x_{2}, y_{2}\right)$ are both single-digit positive integers. The angle between $OA$ and the positive direction of the $x$-axis is greater than $45^{\circ}$, and the angle between $OB$ and the positive direction of the $x$-axis is less than $45^{\circ}$. The projection of $B$ on the $x$-axis is $B'$, and the projection of $A$ on the $y$-axis is $A'$. The area of $\triangle OB'B$ is 33.5 greater than the area of $\triangle OA'A$. Find all such four-digit numbers formed by $x_{1}, y_{1}, x_{2}, y_{2}$, denoted as $\overline{x_{1}x_{2}y_{2}y_{1}}=x_{1} \cdot 10^{3}+x_{2} \cdot 10^{2}+y_{2} \cdot 10 + y_{1}$, and write out the solution process.

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