
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 $\left\{a_{n}\right\}$ has the general term $a_{n} = \tan n \cdot \tan (n-1)$, and for any positive integer $n$, it is given that $a_{1} + a_{2} + \cdots + a_{n} = A \tan n + B n$. Determine the values of $A$ and $B$.

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