
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 number of different distribution methods of 14 calculating devices among 3 people, where one person has 4 types and the other two have 5 types each, is given by the expression $\frac{{C_{14}^{4}C_{10}^{5}C_{5}^{5}A_{3}^{3}}}{{A}_{2}^{2}}$.

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