feat(api): add system prompt support for LLM completion

Separate prompt generation into system and user prompts for better LLM instruction following. Backend now builds a detailed system prompt with constraints for math formatting, code block handling, boundary newlines, and OCR safety, while user prompt contains context and completion state flags. Added corresponding tests for both modules.

backend/llm.py

@@ -54,26 +54,39 @@ def _extract_message(response) -> tuple[str, str]:
     return content, thinking
 
 
-async def call_ollama(prompt: str, *, tag: str = "default", temperature: float = 0.7, thinking: str = None) -> dict:
+async def call_ollama(
+    prompt: str,
+    *,
+    system_prompt: str = None,
+    tag: str = "default",
+    temperature: float = 0.7,
+    thinking: str = None,
+) -> dict:
     """
     调用 Ollama API 并返回 content 和 thinking。
     """
     start = time.perf_counter()
     start_dt = datetime.now()
     logger.info(
-        "[LLM][%s] request model=%s host=%s prompt_chars=%d temp=%.2f thinking=%s",
+        "[LLM][%s] request model=%s host=%s prompt_chars=%d system_chars=%d temp=%.2f thinking=%s",
         tag,
         OLLAMA_MODEL,
         OLLAMA_HOST,
         len(prompt),
+        len(system_prompt or ""),
         temperature,
         thinking,
     )
 
     try:
+        messages = []
+        if system_prompt and system_prompt.strip():
+            messages.append({"role": "system", "content": system_prompt})
+        messages.append({"role": "user", "content": prompt})
+
         kwargs = {
             "model": OLLAMA_MODEL,
-            "messages": [{'role': 'user', 'content': prompt}],
+            "messages": messages,
             "stream": False,
             "options": {
                 'temperature': temperature,