
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 sequence $\{a\_n\}$ has positive terms, with the first term $a\_1=1$, $S\_n$ is the sum of the first $n$ terms of the sequence, and it satisfies: $a\_nS_{n+1}-a_{n+1}S\_n+a\_n-a_{n+1}= \frac {1}{2}a\_na_{n+1}$, then $\frac {3}{34}S_{12}=$ _____ .

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