
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 \( m, n, t \) (\(m < n\)) are all positive integers, and points \( A(-m,0) \), \( B(n,0) \), \( C(0,t) \), and \( O \) is the origin. It is given that \( \angle ACB = 90^\circ \), and:
\[ 
OA^2 + OB^2 + OC^2 = 13(OA + OB - OC).
\]
1. Find the value of \(m + n + t\).
2. If a quadratic function passes through points \( A, B, \) and \( C \), find the expression of this quadratic function.

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