
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
Consider the sequence \(a_1, a_2, a_3, \cdots, a_n, \cdots \) which satisfies \(a_1 = a_2 = 1\), \(a_3 = 2\), and for any natural number \(n\), \(a_n \cdot a_{n+1} \cdot a_{n+2} \neq 1\). Additionally, it holds that \( a_n \cdot a_{n+1} \cdot a_{n+2} \cdot a_{n+3} = a_n + a_{n+1} + a_{n+2} + a_{n+3} \). What is the value of \(a_1 + a_2 + \cdots + a_{100}\)?

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