
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
Suppose {a, b, c} denotes the average of a, b, and c, and [a, b] denotes the average of a and b. What is {{[2, 2], 3, 1} [1, 2] 1}?
**A)** \(\frac{1}{2}\)  
**B)** \(\frac{2}{3}\)  
**C)** 1  
**D)** \(\frac{3}{2}\)  
**E)** 2

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