
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
Tom decides to create a sequence starting from a positive integer $n$. He continually subtracts the largest possible even integer square from the current number until he reaches zero. For example, starting with $n = 76$, his sequence might look as follows (one possible example):

\[\begin{array}{ccccc} 
{} & {} & {} & {} & 76 \\
76 & - & 6^2 & = & 40 \\
40 & - & 6^2 & = & 4 \\
4 & - & 2^2 & = & 0 \\
\end{array}\]

Determine the smallest integer $N$ for which Tom’s sequence has exactly $7$ numbers, including $N$ and $0$.
A) 160
B) 164
C) 168
D) 172

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