
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 a theme park design, there is a "flower" pattern made by cutting a sector from a circle with a radius of $3$ cm, which forms the 'petal'. The removed sector has a central angle of $45^\circ$. What is the total perimeter of the pattern including the two straight edges?
A) $\frac{23}{4}\pi + 6$
B) $\frac{21}{4}\pi + 6$
C) $\frac{19}{4}\pi + 6$
D) $\frac{21}{4}\pi + 4$
E) $\frac{20}{4}\pi + 5$

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