
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
Given a sequence $\{a\_n\}$, where $a\_1=1$, $a\_{2n}=n-a\_n$, and $a\_{2n+1}=a\_n+1$, find the sum of $a\_1+a\_2+a\_3+...+a\_{100}$.

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