
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 \(x\) is an integer that satisfies the following congruences:
\[
4 + x \equiv 2^2 \pmod{3^3}, \\
6 + x \equiv 3^2 \pmod{5^3}, \\
8 + x \equiv 5^2 \pmod{7^3}.
\]
What is the remainder when \(x\) is divided by \(105\)?

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