
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
In one variation of chess called Fischer Random Chess, the initial positions of the pieces are determined randomly with the following rules:

- The white pieces must be placed on squares a1, b1, ..., h1.
- The king must be placed between the two rooks.
- The two bishops must be placed on squares of opposite colors.
- The black pieces must be placed on squares a8, b8, ..., h8, in the same order as the white pieces.

How many different starting positions are possible?

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