
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 sequence of numbers is written on the blackboard: \(1, 2, 3, \cdots, 50\). Each time, the first 4 numbers are erased, and the sum of these 4 erased numbers is written at the end of the sequence, creating a new sequence. This operation is repeated until there are fewer than 4 numbers remaining on the blackboard. Determine:
1. The sum of the numbers remaining on the blackboard at the end: $\qquad$ 
2. The last number written: $\qquad$

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