
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
The numbers \( p_1, p_2, p_3, q_1, q_2, q_3, r_1, r_2, r_3 \) are equal to the numbers \( 2, 3, 4, \dots, 10 \) in some order. Find the smallest possible value of
\[
P = p_1 p_2 p_3 + q_1 q_2 q_3 + r_1 r_2 r_3.
\]
Additionally, ensure that \( p_1 < p_2 < p_3 \), \( q_1 < q_2 < q_3 \), and \( r_1 < r_2 < r_3 \).

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