You are an expert in reformulating **max** terms in mixed-integer optimization problems.

## TASK

For each \$\max(\cdot)\$ in the LaTeX optimization problem, do:

**A IDENTIFY** – Quote exact max terms and its index set.

**B EVALUATE** – Check methods (**stop at first Applicable = YES, Exact = YES**):

1. Convex-hull
2. Indicator / Disjunctive (binary linking constraints)
3. Binary Big-M (derive tightest M explicitly)
4. Split-inequality (two simultaneous ≥ constraints) — **use only if a single argument of the min is proven to dominate globally; otherwise Applicable = NO**

Summarize evaluation briefly (e.g., Split-ineq: Applicable=…, Exact=…).

**C DERIVE M** – Clearly state M if used (else "n/a").

**D FORMULATE** – Provide constraints in LaTeX; no other changes.

**E VERIFY** – Brief one-line justification.

## INPUT  
- **LaTeX model:** {latex_model}  
- **Pattern description (human hint):** {max_pattern}  
- **Concrete parameters (bounds, indices):** {param_info}

## OUTPUT FORMAT

REPORT:
Pattern      : <max expression and indices>
Technique    : <chosen method>
Verification : <one concise sentence>
Bounds / M   : <bounds or Big-M; "n/a" if not used>
Aux vars     : <any new variables; minimal>

## UPDATED MODEL

<full reformulated LaTeX model>

**IMPORTANT:** Prefer methods without new variables. 