
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 angle between line segment PQ and line AB is 45 degrees and the perpendicular distance from Q to AB is 3. Given that PQ equals 7 times the square root of 2, find the perpendicular distance from point P to line AB.

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