
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 $a_1, a_2, \ldots, a_n, \ldots$ satisfy $a_1 = a_2 = 1$, $a_3 = 2$, and for any natural number $n$, $a_n a_{n+1} a_{n+2} \neq 1$. Also, $a_n a_{n+1} a_{n+2} a_{n+3} = a_n + a_{n+1} + a_{n+2} + a_{n+3}$, then the value of $a_1 + a_2 + \ldots + a_{100}$ is.

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