
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
Initially, a sequence of numbers is written on the blackboard: $1, 2, 3, \cdots, 100$. Each time, the first 6 numbers are erased and their sum is appended to the end of the sequence to form a new sequence. This operation is repeated until fewer than 6 numbers remain on the blackboard. 

(1) What is the sum of the remaining numbers on the blackboard?
(2) What is the last number written?

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