
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 courier service charges $15$ cents for sending a package weighing up to 2 pounds. For every pound over 2 pounds, the service costs an additional $5$ cents per pound. Draft a formula to calculate the total cost $C$ in cents for a package weighing $P$ pounds, where $P$ is a positive integer.
A) $C = 15 + 5(P-2) \quad \forall P$
B) $C = 15P$
C) $C = 15 + 5P$
D) $C = \begin{cases} 15 & \text{if } P \leq 2 \\ 15 + 5(P - 2) & \text{if } P > 2 \end{cases}$

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