
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
Let  $AH$  be the altitude of a given triangle  $ABC.$  The points  $I_b$  and  $I_c$  are the incenters of the triangles  $ABH$  and  $ACH$  respectively.  $BC$  touches the incircle of the triangle  $ABC$  at a point  $L.$  Find  $\angle LI_bI_c.$ 

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