
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 \( \triangle ABC \), \( \angle C = 120^\circ \) and \( AB = 15 \). A square \( ABXY \) and a rectangle \( CBWZ \) where \( BW:WZ =  3:2 \) is constructed outside of the triangle on sides \( AB \) and \( CB \) respectively. If points \( X \), \( Y \), \( Z \), and \( W \) all lie on a circle, what is the perimeter of triangle \( \triangle ABC \)?
A) \( 15+9k \)
B) \( 15+8k \)
C) \( 15+5k \)
D) \( 15+10k \)

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