
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
We know  $\mathbb Z_{210} \cong \mathbb Z_2 \times \mathbb Z_3 \times \mathbb Z_5 \times \mathbb Z_7$ .
Moreover,\begin{align*}
	53 & \equiv 1 \pmod{2} 
	53 & \equiv 2 \pmod{3} 
	53 & \equiv 3 \pmod{5} 
	53 & \equiv 4 \pmod{7}.
\end{align*}
Let 
\[ M = \left(
	\begin{array}{ccc}
		53 & 158 & 53 
		23 & 93 & 53 
		50 & 170 & 53
	\end{array}
	\right). \]
Based on the above, find  $\overline{(M \mod{2})(M \mod{3})(M \mod{5})(M \mod{7})}$ .

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