
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 shopping mall plans to distribute a total of 50 new energy-saving desk lamps of type $A$ and type $B$. The purchase price and selling price of these two types of desk lamps are shown in the table below:

|          | Type $A$ | Type $B$ |
|----------|----------|----------|
| Purchase Price (in yuan per lamp) | $40$ | $65$ |
| Selling Price (in yuan per lamp) | $60$ | $100$ |

1. If the shopping mall spends a total of $2500$ yuan on purchasing these lamps, how many lamps of each type were purchased?
2. Assuming the profit from selling each type of lamp remains constant, if the total profit from selling these lamps is at least $1400$ yuan, how many lamps of type $B$ should be purchased at least?

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