
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 $b$, if the graph of the function given by the formula passes through the point with coordinates $(3, 10)$:

1) $y = x + b$;
2) $y = 3x + b$;
3) $y = -\frac{1}{3}x + b$;
4) $y = -\frac{1}{2}x + b$.

Express the function by formula where the graph is a straight line passing through points $A$ and $B$:

1) $A(-6, -3)$, $B(2, -3)$;
2) $A(-4, -4)$, $B(3, 3)$;
3) $A(2, 2)$, $B(0, 4)$;
4) $A(3, -8)$, $B(-5, 32)$.

Using steel wire with a diameter of 5 mm, a cylindrical helical spring with a height of 122 mm needs to be made. Find the number of coils of the spring if the gap between the coils of the unloaded spring should be 8 mm.

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