
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
A school has six classes in one day: Chinese, Mathematics, Foreign Language, History, Politics, and Physical Education. Among all possible arrangements, what is the probability that Mathematics is not the last class, and Physical Education is not the first class?

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