
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 particle is located on the coordinate plane at  $ (5,0)$ . Define a *move* for the particle as a counterclockwise rotation of  $ \pi/4$  radians about the origin followed by a translation of  $ 10$  units in the positive  $ x$ -direction. Given that the particle's position after  $ 150$  moves is  $ (p,q)$ , find the greatest integer less than or equal to  $ |p|\plus{}|q|$ .

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