
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
Robert has 5 indistinguishable copper coins and 5 indistinguishable brass coins. Each coin has an engraving of one face on one side, but not on the other. He wants to stack these 10 coins into a single stack, with no two adjacent coins being face to face, and ensuring that the top coin of the stack is not of the same type as the bottom coin. Find the number of possible distinguishable arrangements of the 10 coins.

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