
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
Ada starts with a positive number $n$ and creates a sequence where each number is derived by subtracting the largest possible perfect square less than or equal to the number at hand until zero is reached. For instance, starting with $n = 60$, the sequence would include $60 \rightarrow 60 - 7^2 = 11 \rightarrow 11 - 3^2 = 2 \rightarrow 2 - 1^2 = 1 \rightarrow 1 - 1^2 = 0$ and so on. Determine the smallest integer $N$ such that Ada's sequence has exactly 10 numbers, and find the last digit of $N$.
A) 1 
B) 2 
C) 5
D) 6 
E) 9

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