
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
Let {$a_n$} be a geometric sequence with positive terms, and let $S_n$ be the sum of the first $n$ terms. Given that $a_3 = 4$ and $a_4a_5a_6 = 2^{12}$,  
(Ⅰ) find the first term $a_1$ and the common ratio $q$;  
(Ⅱ) if $S_{n} = 2^{10} - 1$, find the value of $n$.

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