
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 smallest three-digit number that satisfies the following system of congruences:
\begin{align*}
5x &\equiv 15 \pmod{10} \\
3x + 4 &\equiv 7 \pmod{8} \\
-3x+2 &\equiv x \pmod{17}
\end{align*}

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