
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

Four chips are placed along a line. You have a board with 36 squares, on which 4 chips are positioned along a single line in such a way that every square on the board is on the same horizontal, vertical, or diagonal line with at least one of the chips. In other words, if we consider our chips as chess queens, then every square on the board is attacked by at least one queen. The puzzle is to determine how many ways you can place 4 chips along a line so that every square is on the same line with one of the chips.

Two positions are considered different if the sets of 4 squares occupied by the chips are at least partially different. For example, in the illustration, all chips can be shifted to the adjacent row or placed on any one of the two central rows. We thus found 4 different solutions that can be transformed into each other by rotations and reflections. Remember, the chips must always be placed along some line.

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