
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
Determine the value of \(N\) given that each row and two columns in the grid forms distinct arithmetic sequences.

[asy]
unitsize(0.35inch);
draw((0,0)--(7,0)--(7,1)--(0,1)--cycle);
draw((1,0)--(1,1));
draw((2,0)--(2,1));
draw((3,0)--(3,1));
draw((4,0)--(4,1));
draw((5,0)--(5,1));
draw((6,0)--(6,1));
draw((6,2)--(7,2)--(7,-4)--(6,-4)--cycle);
draw((6,-1)--(7,-1));
draw((6,-2)--(7,-2));
draw((6,-3)--(7,-3));
draw((3,0)--(4,0)--(4,-3)--(3,-3)--cycle);
draw((3,-1)--(4,-1));
draw((3,-2)--(4,-2));
label("25",(0.5,0.5),S); // Changed start point of row sequence
label("10",(3.5,-1.2),S); // Changed first column elements
label("18",(3.5,-2.2),S); // Maintained for consistent arithmetic sequence
label("$N$",(6.5,1.5),S);
label("-23",(6.5,-3.2),S); // Changed end point of second column for increased complexity
[/asy]

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