
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
Let 100 real numbers $a_1$, $a_2$, $a_3$, …, $a_{100}$ satisfy $(n-2)a_n - (n-1)a_{n-1} + 1 = 0$ ($2 \leq n \leq 100$), and it is known that $a_{100} = 199$. Find the value of $a_1 + a_2 + a_3 + \ldots + a_{100}$.

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