
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 company plans to sponsor three college students for their entrepreneurial projects. It has hired two experts to independently review each student's business plan. Assume the probability of a review resulting in either "support" or "not support" is $\frac{1}{2}$. If a student receives two "supports", they will be given a startup fund of 100,000 yuan; if they receive one "support", they will be given 50,000 yuan; if they do not receive any "support", they will not be funded. Calculate:  
(1) The probability that the total sponsorship amount from the company is zero;  
(2) The probability that the total sponsorship amount from the company exceeds 150,000 yuan.

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