
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
Consider \([a\,b]\) as the average of \(a\) and \(b\), and \(\{a\,b\,c\,d\}\) as the weighted average where \(a\), \(b\), \(c\), and \(d\) have weights \(1:2:1:2\) respectively. Calculate the value of \(\{\{2\,2\,1\,1\}\,[1\,2]\,0\,2\}\).
A) \(\frac{8}{7}\)
B) \(\frac{15}{11}\)
C) \(\frac{17}{12}\)
D) \(\frac{11}{10}\)
E) \(\frac{16}{9}\)

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