
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 real number $x$, the real number $y$ that satisfies "0≤y<1 and x−y is an integer" is called the fractional part of the real number $x$, denoted as $〈x〉$. For a real number $a$, the infinite sequence ${a_n}$ satisfies the following conditions:
1) $a_1=〈a〉$;
2) $a_{n+1}= \begin{cases} 〈\frac{1}{a_n}〉 (a_n \neq 0) \\ 0 (a_n = 0) \end{cases}$
(I) When $a = \sqrt{2}$, the general term formula of the sequence ${a_n}$ is _____;
(II) When $a > \frac{1}{2}$, for any $n \in \mathbb{N}^*$, $a_n = a$, then the value of $a$ is _____.

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