
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 that the sum of the first $n$ terms $S_n$ of a geometric sequence of positive numbers $\{a_n\}$ satisfies $S_{n+2}= \frac {1}{4}S_{n}+ \frac {3}{2}$.

$(1)$ Find the first term $a_1$ and the common ratio $q$ of the sequence $\{a_n\}$;  
$(2)$ If $b_n=na_n$, find the sum of the first $n$ terms $T_n$ of the sequence $\{b_n\}$.

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