
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
Chongqing hotpot, also known as tripe hotpot or spicy hotpot, is one of the traditional ways of eating in China. It originated on the banks of the Jialing River in Chongqing at the end of the Ming Dynasty and the beginning of the Qing Dynasty. This dish was also a rough dining style for dock workers and boatmen at Chaotianmen and other docks. The main ingredients include beef tripe, pig throat, duck intestines, and beef blood. Today, Chongqing hotpot has become a shining business card for Chongqing. During the May Day holiday, Xiao Mei, Xiao Hong, and Xiao Li traveled to Chongqing. When they returned home, they planned to buy hotpot base materials as souvenirs. A certain store has a total of $a$ different brands of hotpot base materials, including Qiaotou brand hotpot, De Zhuang brand hotpot, Qiu Xia brand hotpot, etc. Each brand has only three flavors: spicy, clear soup, and mushroom soup. The price of the spicy flavor for each brand of hotpot base material is $25$ yuan per pack, the price of the clear soup flavor is $m$ yuan per pack, and the price of the mushroom soup flavor is $n$ yuan per pack. It is known that $33\leqslant m \lt n\leqslant 37$, where $m$ and $n$ are both positive integers. Xiao Mei and Xiao Hong each spent $600$ yuan at checkout. They bought different quantities of mushroom soup flavor hotpot base materials. Xiao Li spent $700$ yuan. They each bought one pack of each flavor for each brand, and for the same brand, they chose different flavors. If all three flavors of hotpot base materials were purchased, what is the maximum amount Xiao Li could have spent on buying clear soup and mushroom soup flavor hotpot base materials?

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