
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
In response to the national strategy of "precision assistance loans and industrial relief," the city is recruiting voluntary promoters of the "Support Policies" across the city. From 500 volunteers aged between $[20, 45]$, 100 volunteers were randomly selected. The age frequency distribution histogram is shown.

(1) Find the value of $x$ in the diagram.
(2) From the 100 selected volunteers, stratified sampling will be used to select 10 volunteers to participate in a promotional event at the central square. Three of these 10 volunteers will be chosen to serve as main persons in charge. Let $X$ be the number of these 3 volunteers who are "under 35 years old." Find the distribution and mathematical expectation of $X$.

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