
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 any real numbers \( x_{0} > x_{1} > x_{2} > x_{3} > 0 \), to ensure the inequality \( \log_{x_{1}} 1993 + \log_{x_{2}} 1993 + \log_{x_{3}} 1993 \geq k \log_{x_{0}} 1993 \) always holds, find the maximum value of \( k \).

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