
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
Regular octagon $ABCDEFGH$ is divided into eight smaller equilateral triangles, such as $\triangle ABJ$, where $J$ is the center of the octagon. By connecting every second vertex starting from $A$, we obtain a larger equilateral triangle $\triangle ACE$. Compute the ratio of the area of $\triangle ABJ$ to the area of $\triangle ACE$.

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