
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
Given that  $5r+4s+3t+6u =100$ , where  $r\ge s\ge t\ge u\ge 0.$  are real numbers,
find, with proof, the maximum and minimum possible values of  $r+s+t+u$ .

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