
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 board  $64$  inches long and  $4$  inches high is inclined so that the long side of the board makes a  $30$  degree angle with the ground. The distance from the ground to the highest point on the board can be expressed in the form  $a+b\sqrt{c}$  where  $a,b,c$  are positive integers and  $c$  is not divisible by the square of any prime. What is  $a+b+c$ ?

*Author: Ray Li*

<details><summary>Clarification</summary>The problem is intended to be a two-dimensional problem. The board's dimensions are 64 by 4. The long side of the board makes a 30 degree angle with the ground. One corner of the board is touching the ground.</details>

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