
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
in a right-angled triangle  $ABC$  with  $\angle C=90$ , $a,b,c$  are the corresponding sides.Circles  $K.L$  have their centers on  $a,b$  and are tangent to  $b,c$ ; $a,c$  respectively,with radii  $r,t$ .find the greatest real number  $p$  such that the inequality $\frac{1}{r}+\frac{1}{t}\ge p(\frac{1}{a}+\frac{1}{b})$ always holds.

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