
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 television manufacturing company has two models of televisions, A and B, participating in a rural discount campaign. If the company allocates the value of models A and B at a and b thousand Yuan, respectively, then the subsidy given to the farmers for buying these television sets will be $\frac{1}{10}a$ and $m\ln(b+1)$ thousand Yuan, respectively (where $m > 0$ is a constant). Knowing that the company allocates a total value of 100 thousand Yuan for models A and B, with neither type having an allocated amount less than 10 thousand Yuan,
(1) Please choose an independent variable, represent the farmers' total subsidy as a function of this variable, and determine its domain;
(2) Find the amount of model B's allocated funds in thousand Yuan that will maximize the farmers' total subsidy.

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