
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 now has 5 indistinguishable gold coins and 5 indistinguishable silver coins. Each coin has an engraving of a face on one side. He wants to stack all 10 coins on a table into a single stack such that no sequence of three or more adjacent coins are of the same face. Find the number of possible distinguishable arrangements of the 10 coins.

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