
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  $x_1, x_2, . . . , x_{2022}$  be nonzero real numbers. Suppose that  $x_k + \frac{1}{x_{k+1}} < 0$  for each  $1 \leq k \leq 2022$ , where  $x_{2023}=x_1$ . Compute the maximum possible number of integers  $1 \leq n \leq 2022$  such that  $x_n > 0$ .

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