
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 circle $C$: $x^{2}+(y+1)^{2}=5$, and line $l$: $mx-y+1=0 (m\in R)$
(1) Determine the relationship between line $l$ and circle $C$;
(2) Suppose line $l$ intersects circle $C$ at points $A$ and $B$. If the slope angle of line $l$ is $120^{\circ}$, find the length of chord $AB$.

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