
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
Suppose that $x$ is an integer that satisfies the following congruences:
\[
4 + x \equiv 3^2 \pmod{2^3}, \\
6 + x \equiv 2^3 \pmod{3^3}, \\
8 + x \equiv 7^2 \pmod{5^3}.
\]
What is the remainder when $x$ is divided by $30$?

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