
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
Given a sequence $\{a_n\}$ that satisfies: for any $n \in \mathbb{N}^*$, there are only a finite number of positive integers $m$ such that $a_m < n$, and let the number of such $m$ be denoted as $(a_n)^+$. Then, a new sequence $\{(a_n)^+\}$ is obtained. For example, if the sequence $\{a_n\}$ is $1, 2, 3, \ldots, n, \ldots$, then the sequence $\{(a_n)^+\}$ is $0, 1, 2, \ldots, n-1, \ldots$. Given that for any $n \in \mathbb{N}^+$, $a_n = n^2$, find $(a_5)^+$ and $((a_n)^+)^+$.

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