
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
Petya wants to place 99 coins on a \(2 \times 100\) board so that no two coins are in adjacent cells (sharing an edge) and each cell contains at most one coin. How many ways are there to place the coins?

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