
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
[IMO 2007 HKTST 1](http://www.mathlinks.ro/Forum/viewtopic.php?t=107262)
Problem 1

Let  $p,q,r$  and  $s$  be real numbers such that  $p^{2}+q^{2}+r^{2}-s^{2}+4=0$ . Find the maximum value of  $3p+2q+r-4|s|$ .

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