
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
School purchased a batch of energy-saving lamps. It is known that 1 type A energy-saving lamp and 3 type B energy-saving lamps cost a total of 26 yuan; 3 type A energy-saving lamps and 2 type B energy-saving lamps cost a total of 29 yuan. 
(1) Find the price of one type A energy-saving lamp and one type B energy-saving lamp respectively.
(2) The school plans to purchase a total of 50 lamps of these two types, with the quantity of type A lamps not exceeding 3 times the quantity of type B lamps, and not less than 2 times the quantity of type B lamps. How many purchasing plans are there, and which plan is the most cost-effective?

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