Recent advances in spoken dialogue language models have shifted from turn-based to full-duplex designs, where the model continuously listens to the user while generating responses. However, existing duplex backbones still lack a native channel for in-conversation planning and tool calling, leaving real-time agentic behaviour either tied to turn boundaries or relegated to an external cascade. We propose DuplexSLA, a native full-duplex Speech-Language-Action foundation model that decodes assistant audio together with a structured action stream on a shared 160 ms chunk timeline. DuplexSLA is built on a dual-stream three-channel formulation: a continuous user audio channel, a discrete assistant audio channel, and a rate-limited textual action channel, all decoded jointly by a single backbone, so that listening, speaking, planning, and tool calling unfold on one shared clock. Two capabilities define the model: (1) semantic-driven turn-taking control, where interruption, pause, and backchannel are handled inside the same backbone instead of by an external semantic VAD; and (2) in-conversation planning and tool calling, where planning text and structured tool calls are emitted on the action channel without halting assistant audio, so that multi-action and backchannel-triggered tool use are interleaved with ongoing speech. To evaluate these capabilities together, we further construct DuplexSLA-Bench, a duplex benchmark covering pause, interrupt, and backchannel turn-taking together with three styles of in-conversation tool calling. Our project page, interactive demos, and the DuplexSLA-Bench evaluation suite are publicly available at https://github.com/hyzhang24/DuplexSLA.