
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 furniture store plans to purchase a certain number of dining tables and dining chairs for sale, with the following information:<br />

|            | Original Purchase Price (¥/unit) | Retail Price (¥/unit) | Set Price (¥/set) |
|------------|----------------------------------|-----------------------|--------------------|
| Dining Table | a | 380 | 940 |
| Dining Chair | a-140 | 160 | |

It is known that the number of dining chairs purchased for 600 yuan is the same as the number of dining tables purchased for 1300 yuan.<br />

(1) Find the value of a;<br />
(2) The store plans to purchase dining chairs in a quantity that is 5 times the quantity of dining tables plus 20 chairs, and the total quantity of dining tables and dining chairs does not exceed 200 units. If half of the dining tables are sold as sets (one table and four chairs per set) and the remaining tables and chairs are sold at retail, how should the store purchase the items to maximize profit? What is the maximum profit?

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