
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 $\{a_n\}$ is an arithmetic sequence, and $a_2=1$, $a_5=-5$.  
$(1)$ Find the general formula for $\{a_n\}$.  
$(2)$ Let $c_n= \frac {5-a_n}{2}, b_n=2^{c_n}$, and denote the sum of the first $n$ terms of the sequence $\{\log _{2}b_n\}$ as $T_n$, find the minimum value of $n$ that satisfies $T_n \geqslant 2016$.

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