
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
$\triangle FGH \sim \triangle IJK$, where $GH = 30\text{ cm}$, $IJ = 15\text{ cm}$, and $JK = 18\text{ cm}$. Find the length of $IK$. Assume the length of $FK$ is 27 cm. Illustrate with a diagram similar to the original, labeling the sides correspondingly.

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