
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
Liam, Mia, and Noah shared an apartment during a month-long stay where they agreed to split all utilities and rent equally. During the month, Liam paid $L$ dollars, Mia paid $M$ dollars, and Noah paid $N$ dollars. If Liam paid less than Noah but more than Mia, how much does Liam need to pay to Noah so they would have equally shared the expenses?
**A)** $\frac{L + M - 2N}{3}$
**B)** $\frac{M + L - 2N}{3}$
**C)** $\frac{M + N - 2L}{3}$
**D)** $\frac{L + N - 2M}{3}$

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