
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
Find the maximum value of  $ x_{0}$  for which there exists a sequence  $ x_{0},x_{1}\cdots ,x_{1995}$  of positive reals with  $ x_{0} \equal{} x_{1995}$ , such that
\[ x_{i \minus{} 1} \plus{} \frac {2}{x_{i \minus{} 1}} \equal{} 2x_{i} \plus{} \frac {1}{x_{i}},
\]
for all  $ i \equal{} 1,\cdots ,1995$ .

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