
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 $y$ is an integer that satisfies the following congruences: 
\begin{align*}
y+4 &\equiv 3^2 \pmod{3^3}, \\
y+4 &\equiv 4^2 \pmod{5^3}, \\
y+4 &\equiv 6^2 \pmod{7^3}.
\end{align*}
What is the remainder when $y$ is divided by $105$?

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