
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
In the geometric sequence $\{a\_n\}$, $a\_n=54$. The sum of the first $n$ terms is $S\_n=80$, and the sum of the first $2n$ terms is $S\_{2n}=6560$.
(1) Find the first term $a\_1$ and the common ratio $q$;
(2) If $A\_1= \frac {π}{4}$, the sequence $\{A\_n\}$ satisfies $A\_n-A\_{n-1}=a\_1\cdot \frac {π}{6}$ $(n\geqslant 2)$, and $c\_n=\tan A\_n\tan A\_{n-1}$. Find the sum of the first $n$ terms of the sequence $\{c\_n\}$, denoted as $T\_n$.

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