
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
The sequence of numbers \( a_1, a_2, a_3, \ldots, a_n, \ldots \) satisfies the relationship \( a_n = a_{n-1} \cdot a_{n-3} \) for \( n = 4, 5, 6, \ldots \). Find \( a_{2019} \), given that \( a_1 = 1 \), \( a_2 = 1 \), \( a_3 = -1 \).

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