
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 \( a_{1}, a_{2}, a_{3}, \cdots, a_{n}, \cdots \) that satisfies \( a_{1}=a_{2}=1 \), \( a_{3}=2 \), and for any positive integer \( n \), \( a_{n} \cdot a_{n+1} \cdot a_{n+2} \neq 1 \). Additionally, \( a_{n} \cdot a_{n+1} \cdot a_{n+2} \cdot a_{n+3} = a_{n} + a_{n+1} + a_{n+2} + a_{n+3} \). Find the value of \( a_{1} + a_{2} + \cdots + a_{100} \).

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