
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
Let angles A, B, and C be the three interior angles of triangle ABC. Given vectors $m = (\sin A + \sin C, \sin B - \sin A)$ and $n = (\sin A - \sin C, \sin B)$, and $m \perp n$.
(1) Find the size of angle C;
(2) If vector $s = (0, -1)$ and vector $t = $, try to find the range of values for $|s + t|$.

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