
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:

\[
\left\{\begin{aligned}
x_{1}+2 x_{2}+2 x_{3}+\cdots+2 x_{100} & =1 \\
x_{1}+3 x_{2}+4 x_{3}+\cdots+4 x_{100} & =2 \\
x_{1}+3 x_{2}+5 x_{3}+\cdots+6 x_{100} & =3 \\
\cdots & \cdots \\
x_{1}+3 x_{2}+5 x_{3}+\cdots+199 x_{100} & =100
\end{aligned}\right.
\]

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