
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 the diagram, six squares form a \( 2 \times 3 \) grid. The middle square in the top row is marked with an \( R \). Each of the five remaining squares is to be marked with an \( R \), \( S \), or \( T \). In how many ways can the grid be completed so that it includes at least one pair of squares side-by-side in the same row or same column that contain the same letter?

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