
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. He wants to stack all 10 coins in a single vertical stack on a table. The arrangement should follow these rules: (1) no two adjacent coins are of the same color, and (2) no two adjacent coins have faces touching each other. Each coin has an engraving of one face on one side, but not on the other. Find the number of possible distinguishable arrangements of the 10 coins.

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