
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 that Ada has a set of identical cubes and makes solids by gluing together 4 of these cubes, such that each of the 4 cubes has a face that coincides with a face of at least one of the other 3 cubes, calculate the number of unique solids that Ada can make using 4 cubes.

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