
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
The dihedral angle between half-planes $\alpha$ and $\beta$, which is intersected by edge $l$, is $120^\circ$. Points $A$ and $B$ are located on edge $l$ with $AC$ and $BD$ within the half-planes $\alpha$ and $\beta$ respectively. Both $AC$ and $BD$ are perpendicular to $l$, and $AB = AC = BD = 1$. Find the length of $CD$.

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