
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 positive integer  $N$  is given. Panda builds a tree on  $N$  vertices, and writes a real number on each vertex, so that  $1$  plus the number written on each vertex is greater or equal to the average of the numbers written on the neighboring vertices. Let the maximum number written be  $M$  and the minimal number written  $m$ . Mink then gives Panda  $M-m$  kilograms of bamboo. What is the maximum amount of bamboo Panda can get? 

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