
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 (a+2x)^n (a belongs to the set of positive real numbers, n belongs to the set of positive integers and n>1),
(1) If n=6, the coefficient of the term containing x^2 in the expanded form of the binomial is 960. Find the value of a.
(2) If the sum of the coefficients of all terms in the expanded form is 3^10, and n+a=12, find the sum of all binomial coefficients in the expanded form.

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