
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
A total of  $731$  objects are put into  $n$  nonempty bags where  $n$  is a positive integer. These bags can be distributed into  $17$  red boxes and also into  $43$  blue boxes so that each red and each blue box contain  $43$  and  $17$  objects, respectively. Find the minimum value of  $n$ .

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