
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
If \( F(n) \) is a function where \( F(1) = F(2) = F(3) = 1 \), and \( F(n+1) = \frac{F(n) \cdot F(n-1) + 1}{F(n-2)} \), calculate the value of \( F(6) \).

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