
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

Solve the following system of equations:

$$
\begin{aligned}
2 x_{1}-2 x_{2} & =A \\
-x_{1}+4 x_{2}-3 x_{3} & =0 \\
-2 x_{2}+6 x_{3}-4 x_{4} & =0 \\
-3 x_{3}+8 x_{4}-5 x_{5} & =0 \\
\vdots & \vdots \\
-(n-2) x_{n-2}+2(n-1) x_{n-1}-n x_{n} & =0 \\
-(n-1) x_{n-1}+2 n x_{n} & =B
\end{aligned}
$$

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