
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 with an engraving on one side only. He plans to arrange these 10 coins in a stack such that:
1. No two gold coins are adjacent.
2. No two adjacent coins are faced engraved side to engraved side.
3. At least one sequence of three consecutive coins must show their engraved side up.
How many distinguishable arrangements of the 10 coins satisfy these conditions?

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