
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
Given a $4 \times 4$ array, where each row and each column is an arithmetic sequence with four terms, with the first term of the first row being $3$ and the fourth term being $21$, and the first term of the fourth row being $15$ and the fourth term being $45$, calculate the value of the square labeled $Y$ located at the center of this array.

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