
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
Find the smallest number  $k$ , such that   $ \frac{l_a+l_b}{a+b}<k$  for all triangles with sides  $a$  and  $b$  and bisectors  $l_a$  and  $l_b$  to them, respectively.

*Proposed by Sava Grodzev, Svetlozar Doichev, Oleg Mushkarov and Nikolai Nikolov*

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