
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 $ABC$ has side lengths $AB=5$, $BC=6$, and $AC=7$. One bug starts from $A$ and crawls clockwise, while another bug starts from $C$ and crawls counterclockwise; the bug from $A$ crawls at a speed of 1 unit per minute and the bug from $C$ crawls at a speed of 2 units per minute. At what point along $BC$ will the two bugs meet for the first time?

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