
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
Find the least positive four-digit solution to the following system of congruences:
\begin{align*}
10x &\equiv 30 \pmod{20} \\
2x + 10 &\equiv 19 \pmod{9} \\
-3x + 1 &\equiv x \pmod{19}
\end{align*}

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