
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
"Jiayuan Craft Store" plans to make a batch of triangular wooden frames with two sides measuring $7$ centimeters and $3$ centimeters, and the third side being an odd number (unit: centimeters).<br/>$(1)$ The total number of triangular wooden frames that meet the above conditions is ______.<br/>$(2)$ If only one of each type of triangular wooden frame is made, and the cost of the wood for making this frame is $8$ yuan per centimeter, how much money is needed to purchase the materials at least? (ignoring joints)

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