
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 ladder of length $L$ is placed in a narrow alley, leaning against opposite walls. At one end, the ladder makes a $60^\circ$ angle with the ground, and at the other end, it makes a $30^\circ$ angle with the ground. If the height at which the ladder touches the first wall is $H$, find the width $d$ of the alley.

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