
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
a) What is the maximum number of non-overlapping $1 \times 3$ strips that can fit on the napkin shown in the picture?
b) What is the minimum number of $1 \times 3$ strips needed to cover the entire napkin if the strips can overlap?

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