
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

A finite sequence of numbers \( x_{1}, x_{2}, \ldots, x_{N} \) possesses the following property:

\[ x_{n+2} = x_{n} - \frac{1}{x_{n+1}} \text{ for all } 1 \leq n \leq N-2. \]

Find the maximum possible number of terms in this sequence if \( x_{1} = 20 \) and \( x_{2} = 16 \).

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