
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 an acute-angled triangle  $ABC$ ,  $AM$  is a median,  $AL$  is a bisector and  $AH$  is an altitude ( $H$  lies between  $L$  and  $B$ ).  It is known that  $ML=LH=HB$ .  Find the ratios of the sidelengths of  $ABC$ .

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