
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 merchant has 600 items of goods with a cost of $m$ each. The goods are divided into two parts and sold using two different sales strategies:<br/>Strategy 1: 200 items are handed over to a live streaming team for live sales. The selling price is set at 2 times the cost minus $5, and 1% of the sales revenue for that day is used as the fee for the entire live streaming team. As a result, all 200 items are sold out that evening.<br/>Strategy 2: The remaining 400 items are sold at a discounted price, set at 2.5 times the cost. The first time, there is a 20% discount, and 100 items are sold. The second time, on top of the first discount, there is another 20% discount, and the remaining items are sold out in a flash.<br/>$(1)$ Express the fee for the live streaming team in Strategy 1 as an algebraic expression in terms of $m$ ______ yuan;<br/>$(2)$ Express the total sales revenue in Strategy 2 as an algebraic expression in terms of $m$;<br/>$(3)$ Express the total profit for the merchant after implementing both sales strategies as an algebraic expression in terms of $m$. (Total profit $=$ Total sales revenue $-$ Total cost)

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