
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
Compute the number of ways a non-self-intersecting concave quadrilateral can be drawn in the plane such that two of its vertices are \((0,0)\) and \((1,0)\), and the other two vertices are two distinct lattice points \((a, b)\), \((c, d)\) with \(0 \leq a, c \leq 59\) and \(1 \leq b, d \leq 5\).

(A concave quadrilateral is a quadrilateral with an angle strictly larger than \(180^{\circ}\). A lattice point is a point with both coordinates integers.)

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