
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 certain building materials market lists the length specifications and corresponding prices of a type of steel pipe as shown in the table below:

| Length (m) | 1 | 2 | 3 | 4 | 5 | 6 |
|------------|---|---|---|---|---|---|
| Price (元/pipe) | 10 | 15 | 20 | 25 | 30 | 35 |

A school needs to make a promotional sign for a triangular support frame. They have already purchased two steel pipes with lengths of $2m$ and $5m$ respectively, and they need to buy one more.

$(1)$ Which lengths of steel pipes are available for selection?

$(2)$ If the perimeter of the triangular support frame needs to be an even number, how much money in total is needed to purchase the steel pipes for making the triangular support frame?

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