
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 gold coins and 5 indistinguishable silver coins. Each coin has an engraving of one face on one side but not on the other. He wants to stack the ten coins on a table into a single stack so that no two adjacent coins are face to face, and no three consecutive coins are of the same color. Find the number of possible distinguishable arrangements of the 10 coins.

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