
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
From thirty points \(A_{1}, A_{2}, \ldots, A_{30}\), located on a straight line \(MN\) at equal intervals, thirty straight roads extend. These roads are situated on one side of the line \(MN\) and form the following angles with \(MN\):

|  | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| \(\alpha\) | \(60^{\circ}\) | \(30^{\circ}\) | \(15^{\circ}\) | \(20^{\circ}\) | \(155^{\circ}\) | \(45^{\circ}\) | \(10^{\circ}\) | \(35^{\circ}\) | \(140^{\circ}\) | \(50^{\circ}\) | \(125^{\circ}\) | \(65^{\circ}\) | \(85^{\circ}\) | \(86^{\circ}\) | \(80^{\circ}\) |
|  | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| \(\alpha\) | \(75^{\circ}\) | \(78^{\circ}\) | \(115^{\circ}\) | \(95^{\circ}\) | \(25^{\circ}\) | \(28^{\circ}\) | \(158^{\circ}\) | \(30^{\circ}\) | \(25^{\circ}\) | \(5^{\circ}\) | \(15^{\circ}\) | \(160^{\circ}\) | \(170^{\circ}\) | \(20^{\circ}\) | \(158^{\circ}\) |

From all thirty points, thirty cars simultaneously set off along these roads at the same speed without turning. Each intersection has a gate. As soon as the first car to reach an intersection passes it, the gate closes, blocking the way for all subsequent cars to that intersection. Which cars will pass through all intersections on their path, and which will be obstructed?

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