
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
A billiard table. (see picture)
A white ball is on  $p_1$  and a red ball is on  $p_2$ . The white ball is shot towards the red ball as shown on the pic, hitting 3 sides first. 
Find the minimal distance the ball must travel.

![Image](http://www.mathlinks.ro/Forum/album_pic.php?pic_id=280)

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