
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
For real numbers  $B,M,$  and  $T,$  we have  $B^2+M^2+T^2 =2022$  and  $B+M+T =72.$  Compute the sum of the minimum and maximum possible values of  $T.$ 

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