
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
An L shape is made by adjoining three congruent squares. The shape can be subdivided into four smaller L shapes, each of which can in turn be subdivided, and so on. If we perform 2005 successive subdivisions, how many of the \(4^{2005}\) L shapes left at the end will have the same orientation as the original one?

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