
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 a circle C with radius $\sqrt {5}$ and its center on the line $l_1: x-y+1=0$, intersects with the line $l_2: \sqrt {3}x-y+1- \sqrt {3}=0$ at points M and N, and $|MN|=\sqrt {17}$  
(1) Find the standard equation of circle C;  
(2) When the x-coordinate and y-coordinate of the center of circle C are both integers, if for any $m\in\mathbb{R}$, the line $l_3: mx-y+ \sqrt {a}+1=0$ always has common points with circle C, find the range of the real number $a$.

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