
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
There are two fair dice and their sides are positive integers \( a_{1}, \ldots, a_{6} \) and \( b_{1}, \ldots, b_{6} \), respectively. After throwing them, the probability of getting a sum of \( 2, 3, 4, \ldots, 12 \) respectively is the same as that of throwing two normal fair dice. Suppose that \( a_{1}+\cdots+a_{6} < b_{1}+\cdots+b_{6} \). What is \( a_{1}+\cdots+a_{6} \)?

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