
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
Let \( a \) be a real number, and the sequence \( a_1, a_2, \cdots \) satisfies:
\[
\begin{array}{l}
a_1 = a, \\
a_{n+1} = 
\begin{cases} 
a_n - \frac{1}{a_n}, & \text{if } a_n \neq 0; \\
0, & \text{if } a_n = 0 
\end{cases} \quad (n = 1, 2, \cdots)
\end{array}
\]

Find all real numbers \( a \) such that for any positive integer \( n \), \( \left|a_n\right| < 1 \).

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