
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 system of equations:

$$
\begin{aligned}
& x_{1} + 12 x_{2} = 15, \\
& x_{1} - 12 x_{2} + 11 x_{3} = 2, \\
& x_{1} - 11 x_{3} + 10 x_{4} = 2, \\
& x_{1} - 10 x_{4} + 9 x_{5} = 2, \\
& x_{1} - 9 x_{5} + 8 x_{6} = 2, \\
& x_{1} - 8 x_{6} + 7 x_{7} = 2, \\
& x_{1} - 7 x_{7} + 6 x_{8} = 2, \\
& x_{1} - 6 x_{8} + 5 x_{9} = 2, \\
& x_{1} - 5 x_{9} + 4 x_{10} = 2, \\
& x_{1} - 4 x_{10} + 3 x_{11} = 2, \\
& x_{1} - 3 x_{11} + 2 x_{12} = 2, \\
& x_{1} - 2 x_{12} = 2.
\end{aligned}
$$

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