
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 and B plays a game on a pyramid whose base is a  $2016$ -gon. In each turn, a player colors a side (which was not colored before) of the pyramid using one of the  $k$  colors such that none of the sides with a common vertex have the same color. If A starts the game, find the minimal value of  $k$  for which  $B$  can guarantee that all sides are colored.

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