
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
Before graduating from a driving school, a student's driving skills are assessed four times. The rules are: assessments are taken in sequence, and once a student passes an assessment, they need not take any further assessments. If student Xiao Li's probabilities of passing each assessment independently form an arithmetic sequence with a common difference of $\frac{1}{8}$, and his probability of passing on the first attempt is no more than $\frac{1}{2}$, and the probability that he passes on the second attempt is $\frac{9}{32}$.

1. Find the probability $P_1$ that Xiao Li passes the assessment on his first attempt;
2. Find the mathematical expectation for the number of assessments Xiao Li takes.

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