
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) Three lines  $l,m,n$  in space pass through point  $S$ . A plane perpendicular to  $m$  intersects  $l,m,n $  at  $A,B,C$  respectively. Suppose that  $\angle ASB = \angle BSC = 45^o$  and  $\angle ABC = 90^o$ . Compute  $\angle ASC$ .
(b) Furthermore, if a plane perpendicular to  $l$  intersects   $l,m,n$   at  $P,Q,R$  respectively and  $SP = 1$ , find the sides of triangle  $PQR$ .

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