
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 narrow alley of width $w$, a ladder of length $10$ m is placed so that it rests against two opposite walls. Resting against one wall at $Q$, it makes a $60^\circ$ angle with the ground. It touches the other wall at $R$ making a $70^\circ$ angle with the ground. Find the width $w$ of the alley.
A) 5 m
B) 7 m
C) 8.42 m
D) 10 m
E) 6 m

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