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

## TASK

For each **bilinear term** appearing in the LaTeX optimization problem, complete steps A–E:

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

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

1. McCormick envelopes (convex hull, 4 inequalities)
2. Disjunctive (binary linking constraints)
3. Binary Big-M (**only if 1–2 fail**, derive tightest M explicitly)

Summarize evaluation briefly (e.g., McCormick: 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):** {bilinear_pattern}
* **Concrete parameters (bounds, indices):** {param_info}

## OUTPUT FORMAT

REPORT:
Pattern      :<bilinear 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 or binaries when possible.
