Repository: langchain
Issue: set_llm_cache doesn't work for AgentExecutors
Labels: 🤖:bug,investigate

### Checked other resources

- [X] I added a very descriptive title to this issue.
- [X] I searched the LangChain documentation with the integrated search.
- [X] I used the GitHub search to find a similar question and didn't find it.
- [X] I am sure that this is a bug in LangChain rather than my code.
- [X] The bug is not resolved by updating to the latest stable version of LangChain (or the specific integration package).

### Example Code

```python
from langchain.agents import AgentExecutor, create_tool_calling_agent, tool
from langchain.globals import set_llm_cache
from langchain_community.cache import SQLiteCache
from langchain_core.prompts import ChatPromptTemplate
from langchain_openai import ChatOpenAI

set_llm_cache(SQLiteCache("test_llm_cache.sqlite"))



prompt = ChatPromptTemplate.from_messages(
    [
        ("system", "You are a helpful assistant"),
        ("placeholder", "{chat_history}"),
        ("human", "{input}"),
        ("placeholder", "{agent_scratchpad}"),
    ]
)
model = ChatOpenAI(model="gpt-4o")

@tool
def magic_function(input: int) -> int:
    """Applies a magic function to an input."""
    return input + 2

tools = [magic_function]

agent = create_tool_calling_agent(model, tools, prompt)
agent_executor = AgentExecutor(agent=agent, tools=tools, verbose=True)
```


### Error Message and Stack Trace (if applicable)

# Test with Agent 
```python3
%%time
agent.invoke({"input":"what is the value of magic_function(3)?","intermediate_steps":[]})
```
_CPU times: user 47.2 ms, sys: 9.25 ms, total: 56.4 ms
Wall time: 1 s_
[ToolAgentAction(tool='magic_function', tool_input={'input': 3}, log="\nInvoking: `magic_function` with `{'input': 3}`\n\n\n", message_log=[AIMessage(content='', additional_kwargs={'tool_calls': [{'id': 'call_LjQj5h58R846IcmFx8KEyZt8', 'function': {'arguments': '{"input":3}', 'name': 'magic_function'}, 'type': 'function'}], 'refusal': None}, response_metadata={'token_usage': {'completion_tokens': 14, 'prompt_tokens': 61, 'total_tokens': 75, 'completion_tokens_details': {'audio_tokens': None, 'reasoning_tokens': 0}, 'prompt_tokens_details': {'audio_tokens': None, 'cached_tokens': 0}}, 'model_name': 'gpt-4o-2024-08-06', 'system_fingerprint': 'fp_90354628f2', 'finish_reason': 'tool_calls', 'logprobs': None}, id='run-8598a1e7-be43-4b08-88ec-f3200d8a4333-0', tool_calls=[{'name': 'magic_function', 'args': {'input': 3}, 'id': 'call_LjQj5h58R846IcmFx8KEyZt8', 'type': 'tool_call'}], usage_metadata={'input_tokens': 61, 'output_tokens': 14, 'total_tokens': 75})], tool_call_id='call_LjQj5h58R846IcmFx8KEyZt8')]

```python3
#second time
%%time
agent.invoke({"input":"what is the value of magic_function(3)?","intermediate_steps":[]})
```
_CPU times: user 6.18 ms, sys: 2.82 ms, total: 9.01 ms
Wall time: 8.82 ms_
[ToolAgentAction(tool='magic_function', tool_input={'input': 3}, log="\nInvoking: `magic_function` with `{'input': 3}`\n\n\n", message_log=[AIMessage(content='', additional_kwargs={'tool_calls': [{'id': 'call_LjQj5h58R846IcmFx8KEyZt8', 'function': {'arguments': '{"input":3}', 'name': 'magic_function'}, 'type': 'function'}], 'refusal': None}, response_metadata={'token_usage': {'completion_tokens': 14, 'prompt_tokens': 61, 'total_tokens': 75, 'completion_tokens_details': {'audio_tokens': None, 'reasoning_tokens': 0}, 'prompt_tokens_details': {'audio_tokens': None, 'cached_tokens': 0}}, 'model_name': 'gpt-4o-2024-08-06', 'system_fingerprint': 'fp_90354628f2', 'finish_reason': 'tool_calls', 'logprobs': None}, id='run-8598a1e7-be43-4b08-88ec-f3200d8a4333-0', tool_calls=[{'name': 'magic_function', 'args': {'input': 3}, 'id': 'call_LjQj5h58R846IcmFx8KEyZt8', 'type': 'tool_call'}], usage_metadata={'input_tokens': 61, 'output_tokens': 14, 'total_tokens': 75})], tool_call_id='call_LjQj5h58R846IcmFx8KEyZt8')]


# Try with AgentExecutor
```python3
%%time
agent_executor.invoke({"input": "what is the value of magic_function(3)?"})
```

> Entering new AgentExecutor chain...
> Invoking: `magic_function` with `{'input': 3}`
> The value of `magic_function(3)` is 5.
> Finished chain.

_CPU times: user 54.2 ms, sys: 6.7 ms, total: 60.9 ms
Wall time: 1.65 s_

{'input': 'what is the value of magic_function(3)?',
 'output': 'The value of `magic_function(3)` is 5.'}

```python3
%%time
agent_executor.invoke({"input": "what is the value of magic_function(3)?"})
```

> Entering new AgentExecutor chain...
> Invoking: `magic_function` with `{'input': 3}`
> The value of `magic_function(3)` is 5.
> Finished chain.

_CPU times: user 37.6 ms, sys: 4.93 ms, total: 42.5 ms
Wall time: 1.54 s_

{'input': 'what is the value of magic_function(3)?',
 'output': 'The value of `magic_function(3)` is 5.'}





### Description

set_llm_cache doesn't work for AgentExecutors

### System Info


System Information
------------------
> OS:  Darwin
> OS Version:  Darwin Kernel Version 24.0.0: Tue Sep 24 23:36:30 PDT 2024; root:xnu-11215.1.12~1/RELEASE_X86_64
> Python Version:  3.12.7 (main, Oct  1 2024, 02:05:46) [Clang 15.0.0 (clang-1500.3.9.4)]

Package Information
-------------------
> langchain_core: 0.3.8
> langchain: 0.3.1
> langchain_community: 0.3.1
> langsmith: 0.1.130
> langchain_anthropic: 0.2.1
> langchain_aws: 0.2.1
> langchain_groq: 0.2.0
> langchain_mistralai: 0.2.0
> langchain_ollama: 0.2.0
> langchain_openai: 0.2.1
> langchain_text_splitters: 0.3.0
> langchain_together: 0.2.0

Optional packages not installed
-------------------------------
> langgraph
> langserve

Other Dependencies
------------------
> aiohttp: 3.10.8
> anthropic: 0.34.2
> async-timeout: Installed. No version info available.
> boto3: 1.35.32
> dataclasses-json: 0.6.7
> defusedxml: 0.7.1
> groq: 0.11.0
> httpx: 0.27.2
> httpx-sse: 0.4.0
> jsonpatch: 1.33
> numpy: 1.26.4
> ollama: 0.3.3
> openai: 1.51.0
> orjson: 3.10.7
> packaging: 24.1
> pydantic: 2.9.1
> pydantic-settings: 2.5.2
> PyYAML: 6.0.2
> requests: 2.32.3
> requests-toolbelt: 1.0.0
> SQLAlchemy: 2.0.35
> tenacity: 8.5.0
> tiktoken: 0.7.0
> tokenizers: 0.20.0
> typing-extensions: 4.12.2