
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
Given the binomial $(x^2+ \frac {1}{2 \sqrt {x}})^n$ ($n\in\mathbb{N}^*$) is expanded, and the sum of the binomial coefficients of the first three terms is 56, find:  
(1) The value of $n$;  
(2) The seventh term of the expansion.

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