
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 the set \(T = \{0,1,2,3,4,5,6\}\) and \(M=\left\{\frac{a_{1}}{7}+\frac{a_{2}}{7^{2}}+\frac{a_{3}}{7^{3}}+\frac{a_{4}}{7^{4}}\right\}\), where \(a_{i} \in \mathbf{T}, i=\{1,2,3,4\}\). Arrange the numbers in \(M\) in descending order. Determine the 2005th number.

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