
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
Determine the smallest four-digit number that satisfies the following system of congruences:

\begin{align*}
3x &\equiv 9 \pmod{18} \\
5x + 20 &\equiv 30 \pmod{15} \\
3x - 4 &\equiv 2x \pmod{35}
\end{align*}

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