
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
In $\triangle ABC$, $D$ is a point on $BC$, $\angle BAD=90^\circ$, $\cos\angle ADC=-\frac{\sqrt{5}}{5}$.
(I) Find the value of $\sin(B-\frac{\pi}{4})$;
(II) If $BD=2DC=2$, find the length of $AC$.

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