
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 triangle $ABC.$ Let $M$ be the midpoint of the arc $BC$ that does not contain $A$ on the circumcircle of triangle $ABC$. Determine the value of:
\[MA^2 + MB^2 + MC^2 - MH^2\]
in terms of the side lengths $a, b, c$ and circumradius $R$ of triangle $ABC$.

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