
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
Read the following text and answer the questions: We know that $\sqrt{2}$ is an irrational number, and irrational numbers are infinite non-repeating decimals, so we cannot write out all the decimal part of $\sqrt{2}$. Since 1 < $\sqrt{2}$ < 2, we can represent the decimal part of $\sqrt{2}$ as $\sqrt{2}$-1. Please answer the following questions:  
(1) The integer part of $\sqrt{29}$ is ______, and the decimal part is ______;  
(2) If the decimal part of 5+$\sqrt{5}$ is a, and the integer part of 5-$\sqrt{5}$ is b, find the value of a+$\sqrt{5}$b.

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