
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
A modified sequence is defined as $b_1 = 1, b_2 = 2, b_3 = 3$, and, for all positive integers $n$, $b_{n+3} = 2b_{n+2} + b_{n+1} - b_{n}$. Calculate $b_{15}$.

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