
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
The sports ground has  the shape of a rectangle  $ABCD$ , with the angle between the diagonals  $AC$  and  $BD$  is equal to  $60^o$  and  $AB >BC$ . The trainer instructed Andriyka to go first  $10$  times on the route  $A-C-B-D-A$ , and then  $15$  more times along the route  $A-D-A$ . Andriyka performed the task, moving a total of  $4.5$  km. What is the distance  $AC$ ?

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