
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
On May 29, 2016, in the 11th round of the Chinese Super League, Chongqing Lifan will host Hebei China Fortune. The Chongqing "Iron Blood Ba Yu" fan association will continue to organize hardcore fans to cheer for Chongqing Lifan at the scene. The "Iron Blood Ba Yu" fan association plans to purchase a total of 500 tickets, including Type A and Type B tickets, with the number of Type A tickets being at least three times the number of Type B tickets.  
(1) Determine the minimum number of Type A tickets the "Iron Blood Ba Yu" fan association must purchase;  
(2) The "Iron Blood Ba Yu" fan association learned from the ticket office that a certain discount will be given to the association. The tickets for this game will be sold to the association at a unified price of $(m+20)$ yuan per ticket. Therefore, the association decides to increase the number of tickets purchased based on the original plan by $(m+10)\%$. After purchasing the tickets, a total of 56000 yuan was spent. Find the value of $m$.

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