
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
Randomly and without replacement, select three numbers \(a_1, a_2, a_3\) from the set \(\{1, 2, \cdots, 2014\}\). Then, from the remaining 2011 numbers, again randomly and without replacement, select three numbers \(b_1, b_2, b_3\). What is the probability that a brick with dimensions \(a_1 \times a_2 \times a_3\) can fit inside a box with dimensions \(b_1 \times b_2 \times b_3\)?

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