
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 a sports complex, there is a rectangular area \(ABCD\) with the longer side \(AB\). The diagonals \(AC\) and \(BD\) intersect at an angle of \(60^\circ\). Runners train on the large circuit \(ACBDA\) or on the small track \(AD\). Mojmír ran ten times around the large circuit, and Vojta ran fifteen times around the small track, in one direction and then fifteen times in the opposite direction. Together they ran \(4.5 \text{ km}\). How long is the diagonal \(AC\)?

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