
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
The sequence $\{a_n\}$ has a sum of the first $n$ terms denoted by $S_n$, and it satisfies $S_n+ \frac {1}{2}a_n=1$. Sequences $\{b_n\}$ and $\{c_n\}$ satisfy $b_n=\log_{3} \frac {a_n^{2}}{4}$ and $c_n= \frac {1}{b_nb_{n+2}}$ respectively.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) The sum of the first $n$ terms of the sequence $\{c_n\}$ is denoted by $T_n$. If the inequality $T_n < m$ holds for any positive integer $n$, find the range of values for $m$.

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