
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 \(a > b > c > d > 0\), to ensure \(\log_{\frac{b}{a}} 2004 + \log_{\frac{c}{b}} 2004 + \log_{\frac{d}{c}} 2004 \geq m \log_{\frac{d}{a}} 2004\) always holds, find the minimum value of \(m\).

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