
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
The cost of labeling the lockers with a 1-digit number is $2$ cents, 2-digit numbers cost $2+4$ cents, 3-digit numbers cost $2+4+6$ cents, and so on. Thus, the cost to number the lockers is given by the expression $\sum_{k=1}^{n}\left(2+4\cdot k\right)$.

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