
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 sequence ${a_n}$, $a_1= \frac {1}{3}$, $\frac {1}{a_{n+1}}= \frac {3}{a_{n}(a_{n}+3)}$, $n\in N_{+}$, and $b_{n}= \frac {1}{3+a_{n}}$, let $P_{n}=b_{1}⋅b_{2}⋅b_{3}…b_{n}$, $S_{n}=b_{1}+b_{2}+b_{3}+…+b_{n}$, then $3^{n+1}P_{n}+S_{n}=$ \_\_\_\_\_\_.

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