
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
 $PQ$  is a diameter of a circle.  $PR$  and  $QS$  are chords with intersection at  $T$ . If  $\angle PTQ= \theta$ , determine the ratio of the area of  $\triangle QTP$  to the area of  $\triangle SRT$  (i.e. area of  $\triangle QTP$ /area of  $\triangle SRT$ ) in terms of trigonometric functions of  $\theta$ 

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