
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 $H$ be the orthocenter of an isosceles triangle $ABC$ with $AB = AC = b$ and $BC = a$. For any point $P$ on the circumcircle of triangle $ABC$,
\[PA^2 + PB^2 - PH^2\]
is constant. Express this constant in terms of the side lengths $a$ and $b$, and the circumradius $R$ of triangle $ABC$.

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