
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 the sequence \( a_1, a_2, \cdots, a_n, \cdots \) be defined such that \( a_1 = a_2 = 1, a_3 = 2 \), and for any positive integer \( n \), \( a_n \cdot a_{n+1} \cdot a_{n+2} \neq 1 \). Also, given that \( a_n \cdot a_{n+1} \cdot a_{n+2} \cdot a_{n+3} = a_n + a_{n+1} + a_{n+2} + a_{n+3} \), find the value of \( a_1 + a_2 + \cdots + a_{100} \).

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