
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
Xiaoli decides which subject to review during her self-study session tonight—history, geography, or politics—based on the result of a mathematical game. The rules of the game are as follows: In the Cartesian coordinate plane, starting from the origin O and ending at the points P<sub>1</sub> (−1, 0), P<sub>2</sub> (−1, 1), P<sub>3</sub> (0, 1), P<sub>4</sub> (1, 1), P<sub>5</sub> (1, 0), she forms 5 vectors. After choosing any two of these vectors, she calculates the dot product y of them. If y > 0, she will review history; if y = 0, she will review geography; and if y < 0, she will review politics.
(1) List all possible values for y.
(2) Calculate the probability of Xiaoli reviewing history and the probability of her reviewing geography.

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