
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
Consider a square $ABCD$ with side length $2$ and diagonals $AC$ and $BD$ intersecting at point $O$. Through a point $P$ on diagonal $BD$, a line is drawn parallel to side $AB$ so that it exactly bisects the area of triangle $ABD$. Determine the distance from $P$ to side $AB$ if the length of the diagonal $BD$ is $2\sqrt{2}$.
A) 0.5
B) 1
C) 1.5
D) 2
E) 2.5

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