
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
Across the face of a rectangular post-it note, you idly draw lines that are parallel to its edges.  Each time you draw a line, there is a  $50\%$  chance it'll be in each direction and you never draw over an existing line or the edge of the post-it note.  After a few minutes, you notice that you've drawn 20 lines.  What is the expected number of rectangles that the post-it note will be partitioned into?

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