
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
Three numbers, $a_1$, $a_2$, $a_3$, are randomly chosen without replacement from the set $\{1, 2, 3, \dots, 100\}$. Another set of three numbers, $b_1$, $b_2$, $b_3$, is chosen from the remaining 97 numbers. We define a new condition where the sum of the dimensions of the box must be at least 10 units larger than the sum of the dimensions of the brick. Compute the probability $p$ that a brick with dimensions $a_1 \times a_2 \times a_3$ can be enclosed in a box with dimensions $b_1 \times b_2 \times b_3$ under the new condition and with sides parallel.

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