
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
Given the following propositions:

1. The number of terms in the expanded form of the product $(a+b+c+d)(p+q+r)(m+n)$ is $24$.
2. The number of five-digit numbers formed by $1$, $2$, $3$, $4$, $5$ without repetition and with neither $1$ nor $2$ adjacent to $5$ is $36$.
3. In a meeting room, there are $8$ seats in the first row. If three people are seated such that each person has an empty seat on both sides, the number of different seating arrangements is $24$.
4. In the expansion $(1+x)^{8}=a_{0}+a_{1}x+…+a_{8}x^{8}$, the number of odd numbers among $a_{0}$, $a_{1}$, $…$, $a_{8}$ is $2$.

Determine the sequence number(s) of the true proposition(s).

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