
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  $ABC$  be an acute-angled triangle and  $P$  be a point in its interior. Let  $P_A,P_B$  and  $P_c$  be the images of  $P$  under reflection in the sides  $BC,CA$ , and  $AB$ , respectively. If  $P$  is the orthocentre of the triangle  $P_AP_BP_C$  and if the largest angle of the triangle that can be formed by the line segments $ PA, PB$ . and  $PC$  is  $x^o$ , determine the value of  $x$ .

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