
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
Two triangles $\triangle FGH \sim \triangle IJK$, where $GH = 30\text{ cm}$. If the length of $IJ$ is $18\text{ cm}$ and side $JK$ is $15\text{ cm}$, find the length of $FG$. Assume $J$ lies between $I$ and $K$.

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