
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
Given that \(\triangle ABC\) is an isosceles triangle, \(AB = AC = \sqrt{2}\), and \(D_1, D_2, \ldots, D_Q\) are \(Q\) points on \(BC\). Let \(m_i = AD_i^2 + BD_i \times D_iC\). If \(m_1 + m_2 + m_3 + \ldots + m_Q = R\), find the value of \(R\).

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