
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
Starting with a positive integer $n$, a sequence is created by following this rule: each term is obtained from the previous one by subtracting the largest perfect square that is less than or equal to the previous term, continuing until reaching zero. For example, if $n=142$, the sequence of 5 terms is:

$$
a_{1}=142, a_{2}=21, a_{3}=5, a_{4}=1, a_{5}=0
$$

since $21=142-11^{2}, 5=21-4^{2}, 1=5-2^{2}$ and $0=1-1^{2}$.

a) Give an example of a sequence that has exactly 6 terms.

b) Find the smallest value of $n$ for which the sequence thus created has exactly 7 terms.

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