
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 integer $x$ that satisfies the following set of congruences:
\begin{align*}
4+x &\equiv 3^2 \pmod{2^3} \\
6+x &\equiv 4^2 \pmod{3^3} \\
8+x &\equiv 6^2 \pmod{5^3}
\end{align*}
Find the remainder when $x$ is divided by $120$.

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